How has the relationship between Macbeth and his wife changed since the death of Duncan? Why aren't they happy?

Actually, their relationship changes before King Duncan's murder. When Macbeth becomes Thane of Cawdor and begins to believe in the witches' prophecy, he writes to Lady Macbeth telling her his amazing news. The audience does not see Macbeth write the letter, but Scene Five begins with Lady Macbeth's reading it aloud. Macbeth's words make it clear he has embraced the prophecy. He calls her "my dearest partner of greatness" and speaks of their "rejoicing." Lady Macbeth's reaction to the letter shows that she and Macbeth share a strong desire for the crown. This is the last time they commune in harmony.

When Macbeth learns of his wife's murderous plans, he first puts them aside, telling her "We will speak further." When he tells her planning to murder Duncan will stop, she attacks him vehemently, even questioning his manhood. She grabs power in their relationship at that point and maintains it until her own emotional unraveling in Act Five. Thus, Macbeth's most tender feelings for his wife are destroyed early in the drama. He sees her as both incredibly cruel and unwomanly. Ironically, his tenderness toward her revives when her guilt destroys her.

Once crowned, Macbeth and his wife cannot enjoy their power; they guard it jealously. Macbeth kills Banquo to prevent Banquo's portion of the witches' prophecy from coming true, that his heirs would rule. Fleance's escape, however, makes Banquo's murder pointless. Murder follows murder until the final destruction of Macbeth and Lady Macbeth.