At the beginning of the story, it appears that Young Goodman Brown does have faith in his wife, due to the description of his intention to "'cling to her skirts and follow her to Heaven.'" After this one night, he vows, he will be almost as good as she; he relies on her goodness to help him achieve his.
However, later in the story, as soon as he hears a voice that might be hers and sees a pink ribbon (like the ones she wears in her cap) on a branch in the forest, he exclaims, "'My Faith is gone!'" and he claims that there is no goodness on earth. In other words, based on speculation and a ribbon, he assumes the worst: that Faith has abandoned him and all her goodness to turn to the Devil and become sinful. He could assume that the Devil is trying to trick him, but he does not. He assumes that the Devil is honest and that it is Faith who is weak. If Brown truly believed in his wife's faith and goodness, then he wouldn't be so quick to doubt her. When Brown does actually see Faith, he cries, "'Look up to Heaven, and resist the Wicked One!'" but he does not know whether she did as he told her.
He suddenly finds himself alone in the forest, and when he walks back to town and spots his wife, he "looked sternly and sadly into her face, and passed on without a greeting." For the remainder of his life, "he shrank from the bosom of Faith," implying that he does not believe that she turned away from the Devil and that he doesn't truly have faith in her. Though he was in the woods too, he doesn't seem to think that she rejected sinfulness as he tried to do, and he remains suspicious of her until his death.