In the book Fahrenheit 451 what are some quotes that explain Mildred and Montag's relationship?

To understand more about Mildred and Montag's relationship, take a look at this quote from part 1:

There had been no night in the last two years that Mildred had not swum that sea, had not gladly gone down in it for the third time.

In other words, this quote suggests that Montag and Mildred do not share any real intimacy and closeness. Her priorities are very different from his: she would rather spend her evenings listening to the Seashell radio alone than be with her husband. This shows the reader that although they are married, they live very separate lives.
This idea of separation is further reinforced when Montag asks Mildred if she will turn off the parlor walls, because he feels sick. In response, Mildred says:

That's my family.

In other words, Mildred feels more of a connection to these characters than she does to real people in her life. She values this "family" more than she values her own husband.
Finally, in this quote from part 3, we get a further glimpse into their relationship:

Even if she dies . . . I don't think I'll feel sad.

Montag is talking to Granger about Mildred. What he has realized is that he does not really love or value his wife. They are so far apart in a mental and emotional sense that their marriage isn't really a marriage at all. They might be together, but that does not mean that they feel any love or connection to one another.