The biggest change we see in these characters in this third act is in their relation to each other. In the previous two acts, when the murder of Duncan was conceived and carried out, Lady Macbeth seemed much the stronger, more determined and more vocal of the two. In a series of bold and even fearsome speeches, she egged her husband on to murder when he appeared vacillating and unwilling to kill his king. Now, in this third act, although still involved in the action, she has notably much less dialogue than previously, and she seems to have far less command over her husband. He, meanwhile, appears to be hardening in his resolve to pursue his bloody course of despatching anyone whom he thinks might still threaten his position, notably Banquo. However, although she helped him so much in the murder of Duncan, he does not confide to her his arrangements to have Banquo killed. She is left to simply ask: 'What's to be done?' and he replies, 'Be innocent of the knowledge,dearest chuck,/Till thou applaud the deed' (III.ii.45-46). In other words, he is telling her that she needn't know anything about the murder of Banquo until after it has happened.
The individual changes in these two characters naturally affect their relationship with one another. As already stated, Macbeth appears to be hardening by this stage in the play. While he agonized so much in the previous two acts over the initial killing of his king, he now does not appear to hesitate to kill further. Concomitant with this, however, is a certain sense of increasing despair on his part which leads him to behave ever more recklessly. This is most apparent, perhaps, when he observes that
...I am in blood
Stepp'd in so far that, should I wade no more,
Returning were as tedious as go o'er.(III. iv. 136-138)
Macbeth here is saying that he's gone so far already in his wicked deeds, that there is no turning back now; to try and retract from his chosen path of murder makes no more sense than in continuing along that path. The use of the word 'tedious' here is notable. It points to a sense of increasing weariness and despondency in Macbeth. In the previous acts, although he abhorred the murder of his king, he still seemed persuaded that ultimately it was a necessary, if tragic means to a worthy cause: the fulfillment of his personal ambition to become king. However, although he still speaks of 'mine own good' (III.ii.135) he now seems to be losing his overall sense of purpose.
It is the change in Lady Macbeth in this act that is really of note, however. In her first appearance in this act, she appears to have undergone a quite astonishing change of demeanour from the previous acts:
Naught's had, all's spent,
When our desire is got without content.
Tis safer to be that which we destroy,
Than by destruction dwell in doubtful joy. (III. ii. 4-7)
In this short but extremely revealing speech, she reflects that she and her husband have really gained nothing from the murder of Duncan, because they have no peace of mind. In fact she even declares it would be better to be dead, destroyed like Duncan, than to have to live with 'doubtful joy'. Obviously, this speech has a moralistic point: no good can come of murdering someone. But it is scarcely short of startling to hear Lady Macbeth uttering these words, after what we have seen of her in the previous acts. And of course, she will eventually be consumed by her guilt to the point of committing suicide. Macbeth, for his part, seems increasingly to lose all interest in her, as he becomes ever more preoccupied with preserving his own position. However, in Act III, although relations between them have shifted (as discussed above), they still appear to be a fairly loving couple.