What impact does Millie have on Montag when he comes home from responding to the fire?

Montag comes home badly shaken up from witnessing the woman at the book burning incinerating herself. However, rather than ask after him, Millie is simply impatient with Montag and wants him to go to sleep. She is so insensitive to his experience that she even asks if he is drunk. This shows she knows something is wrong, but is judging him as at fault for it.
He lies down across the bedroom from her and they are, to Montag's mind, "a winter island separated by an empty sea." She talks about her day to him, but he is too shocked to comprehend what she has to say. A communication gulf, already there, has widened between them. When he wakes up the next morning, he has a moment of epiphany or realization:

And suddenly she was so strange he couldn't believe he knew her at all.

He asks her how they met, but neither can remember, reinforcing Montag's knowledge that they have grown irreconcilably apart—though he will try again to reach her and communicate to her his interest in books.

At the beginning of the novel, Montag witnesses a woman commit suicide by lighting herself on fire while the firemen burn her books. The experience traumatizes Montag, who begins to contemplate the secrets that books must possess that would make a woman commit suicide rather than live without literature. When Montag returns home, Mildred is lying in bed blissfully listening to music on her Seashell radio. Initially, Montag does not know what to say to his wife, who does not pay attention to him. Montag then asks Millie if she remembers where they met. Unfortunately, Millie cannot remember where she met Montag, which reveals how distant the couple is from one another. Montag begins to get upset, and Mildred proceeds to take a few sleeping pills. Her indifference to Montag's presence and lack of concern for his mental state following his traumatic experience at work emphasizes her callous, superficial nature. Mildred's reaction influences Montag to make a drastic change in his life, and he begins by refusing to go to work the next day.