I agree with the above editor's response that the initial relationship between Macbeth and Lady Macbeth is one of respect, passion, and compatibility. Lady Macbeth is clearly interested in helping Macbeth achieve his highest ambition, and Macbeth is clearly in awe of his wife's commitment to helping him become king.
However this relationship changes after Macbeth murders Duncan. Shakespeare suggests these changes quite effectively and efficiently with just a few lines. In Act 3, Lady Macbeth must send a servant to arrange a meeting with her husband. We immediately see a distance between the two of them once Macbeth has established himself as king. Macbeth in contemplating the murder of Banquo refuses to allow his wife to be a conspirator: "Be innocent of the knowledge, dearest chuck, till thou applaud the deed." This is quite a switch from the conspiring couple we saw in Act 1 and in the first part of Act 2. At the end of Act 3 we see Macbeth head toward to the witches for counsel as opposed to his wife.
What caused this separation? this change? I think it lies in the varying degrees of guilt that Lady Macbeth and Macbeth feel after killing Duncan. Macbeth is numb with guilt and regret. He almost immediately wishes he could take back the deed. Lady Macbeth, however, is excited and ready for the opportunities that lie ahead. "A little water clears us of this deed," she tells her husband. Lady Macbeth unwittingly created a monster of her husband. Once he crossed the line from honor to immorality, she lost him. He begins a path of murder and slaughter, hoping to regain his sense of well-being and security, only to find that this path makes him more alienated than ever from all those whom he loved and loved him. Macbeth is incapable of loving anyone after he murdered Duncan.
In Shakepeare's Macbeth, Macbeth and Lady Macbeth appear to be in love and have a genuinely strong relationship--at the beginning of the play, anyway. This doesn't mean they aren't corrupt and that they don't possess warped values, and it doesn't mean they don't use each other to further their goals. But they do seem to be genuinely affectionate toward one another. The enotes Study Guide on the themes of the play says the following:
Oddly, among all of Shakespeare's married couples, the Macbeths of Act I and Act II show the highest degree of bonding and cooperative spirit. The very first time that we see Lady Macbeth, she is reading a letter from Macbeth prefaced by the fond salutation, "Dearest Partner of Greatnesse." There is in the first two acts of the play a mutual admiration between the two, a dual respect based on their shared conviction that the manly Macbeth is fit to be king, while the commanding Lady Macbeth is his natural consort. When Lady Macbeth is first told that Macbeth has executed their plan and killed the king, she cries out "My husband."
Productions of the play generally bear this out. The Macbeths are usually portrayed as affectionate and their relationship filled with physical contact.
And their thought processes, in at least one instance, are uncannily similar. When Macbeth enters the stage after his wife has read his letter outlining the witches' predictions, etc., she greets him with "Great Glamis, worthy Cawdor" (Act 1.5.52) and he greets her with "My dearest love," (Act 1.5.56) and the news that Duncan will be staying at their castle tonight.
They are both thinking the same thing. Lady Macbeth asks:
And when goes hence?
And Macbeth immediately replies:
Tomorrow, as he purposes.
The "as he purposes" demonstrates Macbeth's understanding of Lady Macbeth's implication (that Duncan won't be leaving) and his agreement with her implication. When will Duncan be leaving? He plans to leave tomorrow.
Macbeth and Lady Macbeth appear to be a well-matched couple.