Man, is this relationship bad! I am struck by how intensely bad, yet seemingly normal the relationship is between Guy and Millie. I think that things between them are fine, so long as Status Quo is completely embraced and never questioned. When Guy starts to question his own reality and the surrounding system of which he and Mildred are a part, we begin to see challenge in their relationship. Millie wants things to go back to "the way things were," and Guy is committed to exploring the new consciousness that he has adopted. At the same time, the distance that was probably latent between them emerged into a mammoth sized rift between them. This distance essentially sees them as married, but really having little connection, if any. Guy pursues his own life with his new understanding and Millie takes an overdose of sleeping pills as her way of "dealing" with hers. The really fascinating, and scary, element about their relationship is that as Guy develops as a character in the novel, we see little in way of emotion about the relationship he shared with Mildred. It's almost as if it has been airbrushed out of his emotional memory, making it a really unhealthy relationship in my mind. As he pursues his own new understanding about himself and the world, it seems that this "political" aspiration and exploration supplants all else, even a relationship in the private. Montag uses her overdose as a political element, surmising that there was something odd about the nonchalant way her caretakers dismissed her actions. At this, we can see how the political has subsumed the private in Montag's mind.
To me, this relationship is very one sided. Guy Montag clearly cares about Millie, but she does not care about him. You can see this in the way that they treat each other.
Guy is very concerned about Millie. He is alarmed when she just about kills herself (accidentally) and he wants to try to fix their relationship. He seems to care about her because he tries to get her to read books and such, hoping that this will make her care about her life again. If he didn't care about her, he would not have needed to do this.
By contrast, Millie does not care about Guy. She only cares about the "people" in the parlour walls. Even when Guy is all worried about their relationship, Millie is not. For her, Guy and their relationship are really not important. This shows how she is a true product of her society -- she does not really care about other people.