In the simplest of terms, John faints because he is overcome with what he sees.  His wife has subsumed herself within the wallpaper and the designs she has perceived within it.  As a result, John comes in the room and finds a very intense sight around him:

"What is the matter?" he cried. "For God's sake, what are you doing!"
        I kept on creeping just the same, but I looked at him over my shoulder.
        "I've got out at last," said I, "in spite of you and Jane. And I've pulled off most of the paper, so you can't put me back!"
        Now why should that man have fainted? But he did, and right across my path by the wall, so that I had to creep over him every time!

The fact that he is described as "crying" out when he speaks to his wife, represents how he is unable to fully fathom what he sees.  As a result, his fainting is about the only semi- appropriate response he can generate. Simply put, the sight of the wallpaper torn off and his wife circling around the room as if she is in the wallpaper is too much for him to take. He faints as a direct result of what he sees around him.

The narrator "creeps" because of her perception that she has found a way out of the wallpaper.  Her creative energies had been thwarted with the "rest therapy" prescribed to her.  The narrator had wanted to write, and find some outlet to express her feelings.  However, under "strict" orders she had to "rest."  As a result, her mind became fixated on the wallpaper.  The design of the wallpaper and what she could see in it began to occupy her thoughts: "For outside you have to creep on the ground, and everything is green instead of yellow. But here I can creep smoothly on the floor, and my shoulder just fits in that long smooch around the wall, so I cannot lose my way."  That she does not want to get lost in the pattern of the wallpaper is why she "creeps" around the floor.  She "creeps" in order to stay in line with the wallpaper, and so that she does not become lost in this world.  She has not committed suicide.  At one point, she suggests that she cannot do that because it would be "improper and might be misconstrued."  Rather, she finds a sense of connection to "creeping" around the room and becomes subsumed with the condition offered in the wallpaper.

Whether the narrator has escaped the established medical community's approaches is a matter of concern.  On one hand, I think that a case can be made that the narrator has gone insane.  To argue this, it becomes clear that she has become subsumed by the wallpaper and has lost her sense of rational thought as a result.  However, I think that another good case can be made that she has challenged the establishment's diagnoses.  The narrator did everything asked of her, but the results were disastrous.  She has exposed the failure of the patriarchal system, a condition that her husband was a part of.  This might be why he faints; a feeble response to his own complicity in making his wife the way she is.  At the same time, the narrator has demonstrated how wrong the diagnosis of "simply needing to rest" actually was.  There was something more complex and intricate going on  that John and her brother missed.  She has "escaped" in so far as she has proven the establishment to be futile in understanding her condition."In spite of" men like her husband and brother, the narrator has challenged this institution.  The narrator has demonstrated an effective response to their seemingly transcendental statement of absolutist understanding.  It is in this light where she has "escaped" in a manner of speaking.

The narrator's husband (a doctor), John, has spent the majority of the story diminishing and even undermining the validity of the narrator's mental condition as a product of her imagination and weakness.  She tells us, "John laughs at me, of course, but one expects that in marriage."  A wife expects her husband to laugh at her?!  She is not a child being silly (although he does refer to her once as "little girl"); she is a grown woman experiencing a very real mental illness, not, as John tells all their friends and relatives, "a slight hysterical tendency."  We now understand that the narrator is likely suffering from postpartum depression, a condition that affects many women after the birth of a child.  It is not "slight," and it is not some little trifling illness that women imagine because they are hoping for a rest.  In fact, the narrator hates the rest that her husband forces her to take.  However, John tells her that "no one but [her]self can help [her] out of [her nervous weakness], and that [she] must use [her] will and self-control and not let any silly fancies run away with [her]."  In other words, her husband believes that the narrator's illness is the result of her overactive imagination, her "silly fancies," and a weakness resulting from her lack of "self-control." 

However, in the end, it is he who faints.  It is he who is too weak to face the truth of her condition and too weak to bear himself up under the weight of what his "treatment" has done to her.  The end of the story seems to point to the idea that it is not women who are mentally weak, though they might be (on average) the physically weaker sex; rather, it is men who are mentally weak for failing to realize that there is more to women's medicine than treating generic "hysteria" with rest, isolation, and imprisonment.  By having John faint, Gilman turns the tables on men like the narrator's husband, brother, and even Weir Mitchell, the doctor who John threatens the narrator with.  The narrator has found a way to feel empowered, though it required a complete dissociation with her identity. She now believes herself to be free because she is not trapped behind the wallpaper, but her husband cannot handle that truth she has created in her mind: he is the weak one.

John, the narrator's husband, is a product of his time; he has little understanding of his wife's mental state and how his actions are affecting it. At the end of the story, when she has essentially gone insane, he opens the door to her room and finds her "creeping" around the perimeter, where she has torn the yellow wallpaper away.

"For God's sake, what are you doing!"

I kept on creeping just the same, but I looked at him over my shoulder.

"I've got out at last," said I, "in spite of you and Jane. And I've pulled off most of the paper, so you can't put me back!"

Now why should that man have fainted? But he did, and right across my path by the wall, so that I had to creep over him every time!(Gilman, "The Yellow Wallpaper," library.csi.cuny.edu)

Naturally, John has no idea that the narrator believes a woman to be trapped behind the designs of the wallpaper, or that she has now placed herself into that role. His complete failure to understand her feelings, coupled with what appears to be a complete mental breakdown on her part, is too much for him to handle, and he faints. In this way, he shows that he cannot understand her emotional state, and he becomes a physical obstacle for her to "creep" over instead of a mental or emotional obstacle.

It's somewhat ironic that John, a doctor and man of science, should be the one to faint, when the narrator is supposed to be the one suffering from hysteria. Yet if we put ourselves in John's shoes for a moment, we can see that, under the circumstances, his reaction is entirely appropriate—for there is something undeniably terrifying about seeing one's wife creeping around the room to avoid suspicion for having freed an imaginary woman from the wallpaper.

As a doctor, John will undoubtedly have witnessed a lot of strange behavior among his patients. But he's never seen anything like this before, especially not in his wife, of all people. To see such horrible manifestations of mental instability in someone he cares about—although he has a deeply questionable way of showing it at times—is a truly shocking sight, one that even his robust nervous system cannot handle.

When John finally awakens from his fainting spell, he'll somehow have to deal with his wife's mental illness. He'll have to get used to seeing his wife in a terrible state for which he may not believe there to be a cure—and which he himself helped to cause. In short, he'll have to be strong, which means, among other things, not fainting at the sight of his wife's deranged behavior.

By the time the narrator's husband, John, returns to the house where his wife is being "treated" with the rest cure for her "hysteria"—a sort of catch-all term to describe anxiety or depressive disorders in women at the time—she is no longer herself. She's essentially had a complete mental breakdown where she now believes that she is the woman that she believes she has freed from the wallpaper. Unable to free herself and held practically a prisoner by her husband (who had good intentions but terrible methods), perhaps it is easier to believe that she is a free woman, even if it isn't the objective reality. She says to John,

"I've got out at last [...] in spite of you and Jane[.] And I've pulled off most of the paper, so you can't put me back!"

We've never heard a reference to a "Jane" before—we've met John, the narrator's husband, and Jennie, her sister or sister-in-law—and so it makes sense to assume that Jane is actually the narrator's name. Hearing his wife refer to herself in the third person, as though she no longer recognizes her own identity, could certainly account for John's fainting. He realizes that she has gone completely insane and believes herself to have come out of the wallpaper. Then, she must creep over him as she crawls around the room because he fell right into her path, and she feels that she must continue to circle the room over and over.

By this point in the story, the narrator and main character has essentially lost her mind entirely. She has torn down most of the wallpaper and has, in her mind, "become" one of the women she believed she saw creeping around, trapped behind the pattern in the paper. There are several clues that she has started the creeping early in the story--the long "smooch" all around the room at the same level ("round and round and round--it makes me dizzy!") being one of them. She later states that her shoulder "just fits" in this smooch when she is creeping around the room.

John faints because he has been absent during the main of the room's destruction, and because he believed she was improving up to this point. When he returns home, she has locked the door, inciting panic because he does not know what she is doing. When he finally opens the door, he sees the wallpaper in shreds on the floor and his wife crouched, shoulder against the wall, slinking around the room. Her claim, "I've got out at last...in spite of you... And I've pulled off most of the paper, so you can't put me back!" is ultimately what causes him to faint, likely because he has finally realized the extent of her madness. She believes she is the woman who she "saw" trapped in the paper.

Now, she is "forced" to creep over him because, in her madness, she has taken to the designated track around the room, and she cannot stop her creeping. He faints "right across [her] path by the wall" and this means that in order to continue on her way, she has to step over him.

Throughout Charlotte Perkins Gilman "The Yellow Wallpaper" the reader comes to understand that much of the failure of the treatment of the unnamed narrator's "nervous condition" is due to the Victorian society in which she is held captive by the common law doctrine of femme covert [French for covered, (hidden) woman/wife].  Under this law the husband had virtually total control of his wife's life.  Thus, in every aspect of her marriage, the wife was repressed in this patriarchal society.  Added to this, was the prevailing wisdom of Dr. Weir Mitchell who contended that "post-partum depression" was a myth, and the real condition was only nerves.  For this condition, Mitchell believed in total rest without any mental of physical activity.  And, the narrator's husband John concurs completely with this diagnosis.

So, whenever the narrator pleas with him to allow her to go into the garden, or to have a window open, John refuses.  Compounding this problem, the narrator, made submissive by her repressed social condition, begins to criticize herself,

I get unreasonably angry with John sometimes.  I'm sure I never used to be so sensitive.  I think it is due to this nervous condition.

But John says if I feel so shall neglect proper self-control; so I take pains to control myself--before him, at least, and that makes me tired.

I don't like our room a bit.  I wanted one downstairs that opened on the piazza and had roses all over the window, and such pretty old-fashioned chintz hangings!  But John would not hear of it.

With her husband's domination, the deprivation of anything aesthetic and pleasing, as well as the loss of socialization, the narrator focuses upon "the hideous wallpaper.  Aesthetically repulsed by the lack of symmetry--"I never saw a worse paper in my life--and the "lurid orange and sickly sulphur tint" of its color, the narrator begins to obsess on this wall covering from which she can find no relief. Her concerns then turn inward and she feels that she is "a comparative burden already" to her husband.

Gradually, however, the narrator, a creative, intelligent woman whose talents are depreciated by her repressive husband and who is denied "stimulating people" whom she needs, focuses so intently upon the wallpaper that she imagines exerts "a vicious influence" upon her.  This, then, causes her to feel a sense of antagonism, "impertinence" in the paper with its "unblinking eyes" that are ubiquitous.  From this vision then emanates a "strange, provoking, formless sort of figure" that seeks to be freed from the horizontal bars of the yellow wallpaper.  The narrator initially fears this woman, who is really her emerging sense of self.  In her submissiveness, she wishes "John would take me away from here!"

When she voices her anxiety to her husband, he tells her not to think about it.  More and more she feels trapped until she must free this woman she is behind the bars of the paper.  However, instead of freeing her, the narrator's sense of self enters the wallpaper and is irrevocably trapped.  When her husband knocks, she ignores him, for she is no longer outside the insanity of the paper.  When he breaks down the door, John finds his wife crawling along the baseboard, mentally lost. As she creeps along the baseboard, he perceives her insanity for which he is responsible and faints.  Of course, she does not understand why, and simply continues "to creep over him every time!"