John Proctor and his wife have a tumultuous relationship.
A large part of the reason that these two don’t get a long is that Proctor has not been faithful to his wife. He had an affair with the servant, Abigail. Most wives would not appreciate that. Elizabeth Proctor does not trust him since then, for obvious reasons. She fired the servant, and treats him coldly. If you look at the interaction between the two of them at the beginning of the play, she still has cause to be concerned.
Proctor, his smile widening: Ah, you’re wicked yet, aren’t y’! A trill of expectant laughter escapes her, and she dares come closer, feverishly looking into his eyes. You’ll be clapped in the stocks before you’re twenty. (Act 1, Scene 1)
It’s clear from this that things are not over between the two of them from a physical standpoint. John was a dog and, for all intents and purposes, is still a dog. Basically, there is nothing that can keep them apart because even though his wife dismissed Abigail he still has higher status than the servant girl and he can have her whenever he wants her. So, accusations of witchcraft surrounding the Proctors really have their roots in nothing more exciting than good old-fashioned hanky-panky.
Although John does act somewhat honorably at some points in the play, and Elizabeth does sort of come across as an old shrew, the situation that they get put into is a larger than life exaggeration created by a perfectly normal, albeit immoral, sequence of events created by perfectly human weakness. If John Proctor had been more faithful to his wife, a lot of the madness that took Salem might have not affected them as much or at least not been as centered around the Proctor household so spectacularly.
To continue off of what litteacher8 was saying, John and Elizabeth are still tied to each other; they are still married to each other, and they still do love each other. Through the witch trial, you see the loyalty they have for each other. After Elizabeth is accused of witchcraft by Abigail, John willingly sacrifices his name in order to save her, admitting to the affair to pinpoint the reason why Abigail has blamed Elizabeth.
PROCTOR: (Hanging head, turning front.) In the proper place—where my beasts are bedded. Eight months now, sir, it is eight months. She used to serve me in my house, sir. A man may think God sleeps, but God sees everything. I know it now. I beg you, sir, I beg you—see her for what she is. My wife, my dear good wife took this girl soon after, sir, and put her out on the high road. And being what she is, a lump of vanity, sir…. (Starts to weep.) Excellency, forgive me, forgive me. She thinks to dance with me on my wife’s grave! And well she might!—for I thought of her softly, God help me, I lusted, and there is a promise in such sweat! But it is a whore’s vengeance, and you must see it; I set myself entirely in your hands, I know you must see it now. My wife is innocent, except she know a whore when she see one.
This scene occurs in Act III, when Proctor brings in Mary, Proctor's maid, to testify against Abigail. Abigail has turned the girls again Mary, so Proctor, desperate, states that Elizabeth is innocent. However, Elizabeth wants to protect Proctor's name when she is brought before the court, so she lies to save him, even though he had already stated that Elizabeth does not lie.
DANFORTH: Woman, look at me! Were she slovenly? Lazy? What disturbance did she cause?
ELIZABETH: Your Honor, I… in that time I were sick. And I… My husband is a good and righteous man. He is never drunk, as some are, nor wastin’ his time at the shovelboard, but always at his work… But in my sickness—you see, sir, I were a long time sick after my last baby, and I thought I saw my husband somewhat turning from me. And this girl… (She turns to Abigail.)
DANFORTH: (Shouting.) Look at me!
ELIZABETH: (Weeping.) Aye, sir. Abigail Williams… I came to think he fancied her. And so one night I lost my wits, I think, and put her out on the high road.
DANFORTH: Your husband… did he indeed turn from you?
ELIZABETH: (A plea.) My husband… is a goodly man, sir… (She starts to glance at Proctor.)
DANFORTH: Look at me! To your own knowledge, has John Proctor ever committed the crime of lechery? (In a crisis of indecision she cannot speak.) Answer my question! Is your husband a lecher!
ELIZABETH: (Faintly.) No, sir.
DANFORTH: Remove her. (Proctor and Abigail turn around into scene.)
PROCTOR: Elizabeth, tell the truth, Elizabeth!
DANFORTH: She has spoken. Remove her. (Hale crosses R. following Elizabeth.)
PROCTOR: (Cries out.) Elizabeth, I have confessed it!
ELIZABETH: Oh, John! (Goes out.)
PROCTOR: She only thought to save my name!
Proctor was trying to save Elizabeth from being hanged as a witch, while Elizabeth was trying to save Proctor from being considered an adulterer. The two have a long history together, and at the end, when the other is in trouble, they will still do anything to save each other.