What is the relationship between Ezra and Christine?

The relationship between Ezra and Christine is . . . complicated.
The play trilogy, Mourning Becomes Electra, by Eugene O'Neill, is set in New England at the of the Civil War. At the opening of the first play of the trilogy, The Homecoming, the Mannon family is awaiting the return from the war of Brigadier General Ezra Mannon, the patriarch of the family.
While Ezra was at war, his wife, Christine, had an affair with Adam Brant, a ship captain with possible familial connections with the Mannons. Adam had sworn revenge against the Mannon, but instead falls in love with Christine. Christine promises her daughter, Lavinia—who thought that Adam was in love with her—that she was going to end the affair with Adam, but she had no real intention of doing so.
Now that Ezra has returned home, Christine convinces Adam that in order to maintain their relationship and be married, they must kill Ezra. It's commonly known that Ezra suffers from a heart condition, so Christine and Adam conspire to kill Ezra by replacing his heart medicine with poison.
In a quarrel with Ezra over their failing marriage, Christine confesses her affair with Adam, and she reveals the truth of their relationship.

"You want the truth? You've guessed it! You've used me, you've given me children, but I've never once been yours! I never could be! And whose fault is it? I loved you when I married you! I wanted to give myself! But you made me so I couldn't give! You filled me with disgust!" [Christine, Act 4.]

Christine's confession causes Ezra to have a heart attack. Christine substitutes poison for Ezra's heart medicine. Lavinia rushes into the room, and with his dying breath, Ezra accuses Christine of killing him.

"She's guilty—not medicine!" [Ezra Mannon, Act 4]