I think this is a super question! It can be argued, I think, that Macbeth takes on Lady Macbeth's initial appearance of being a cold-blooded killer as the play goes on, and Lady Macbeth becomes consumed by the guilty thoughts that seem to plague Macbeth early on.
In the first two Acts of the play, Lady Macbeth seems invincible. She asks the powers of darkness to "un-sex" her in Act I, scene v, so that she might be filled "from the crown to the toe top-full/Of direst cruelty." She wants to "stop up the access and passage to remorse," so that she not be shaken from her "fell purpose." And she boldly marches forward, taunting Macbeth for his hesitation as being less than a man, and finally, when he won't return to the crime scene to return the daggers to lie by the dead king, she does it herself. Upon her return to Macbeth in II, ii, she exults victoriously:
My hands are of your colour; but I shame
To wear a heart so white.
Later, after the banquet scene, she all but disappears from the play, returning in Act V, transformed into a guilt-ridden madwoman who is unable to sleep, because she is plagued with dreams about trying to wash the murderous blood from her hands.
Macbeth, on the other hand, seems to develop in exactly the opposite way throughout the play. He begins very suspicious of the plan to murder Duncan and seems to be very disposed to not follow this course of action. In Act I, scene vii, he has a very telling soliloquy in which he confronts all the reasons it's a bad idea to kill Duncan, yet he goes forward because of his ambition. After his skittish performance in the murder of the king, he does wise up and employ henchmen to do the rest of his dirty deeds for him, but he also grows with each murder, to act more and more without conscience.
Finally, in Act V, he has become the sort of emotionless killing machine that Lady Macbeth seemed to be in Act I. In one of the most famous speeches in all of Shakespeare, after he learns of the death of Lady Macbeth, he says that life, essentially, has no meaning. It is "full of sound and fury" but signifies "nothing."
So, yes! I think a case could definitely be made for their exchange of personalities through the course of the events of the play. Please find more details about this topic in the essays linked below.