Who is the family and what are some citations that describe them in Ray Bradbury's Fahrenheit 451?

Mildred, Montag's wife, refers to the characters on the parlour wall shows as her "family." She is more emotionally invested in these shows than she is with her own husband. This is one of the ways Bradbury shows the dangers of technology. Mildred's obsession with these shows and her dependence on sleeping pills has made her a thoughtless, obedient citizen of oppressive authority figures like Beatty. In other words, the government and authorities love for their citizens to be like Mildred. 

Near the end of Part 1, Mildred informs Montag that Clarisse has been killed. The next morning, Montag claims that he is sick and wants to stay home from work. Mildred doesn't like this because he is interrupting her "family." He asks her to turn it off. She replies that she will turn it down but does not turn it down. She can't live without them. 

At the beginning of Part 2, Mildred tries to tell Montag how her "family" are more real than things he finds in books: "my 'family' is people. They tell me things; I laugh, they laugh! And the colours!" In Part 1, Montag asks Mildred to describe some of her family and she gives this similarly vague response: "Well, they-they had this fight, you see. They certainly fight a lot. You should listen. I think they're married. Yes, they're married." With simplistic descriptions such as "colors" and "fighting," it sounds like mindless entertainment. 

The morning after her overdose, she gives Montag a summary of the latest interactive show: 

"Well, this is a play comes on the wall-to-wall circuit in ten minutes. They mailed me my part this morning. I sent in some box-tops. They write the script with one part missing. It's a new idea. The home-maker, that's me, is the missing part. When it comes time for the missing lines, they all look at me out of the three walls and I say the lines: Here, for instance, the man says, `What do you think of this whole idea, Helen?' And he looks at me sitting here centre stage, see? And I say, I say --" She paused and ran her finger under a line in the script. " `I think that's fine!' And then they go on with the play until he says, `Do you agree to that, Helen!' and I say, `I sure do!' Isn't that fun, Guy?" 

This show makes Mildred feel like she is a part of her family. Note, however, that she is scripted what to say. This underscores the idea that Mildred is generally brainwashed. Her lines in the interactive show are scripted. And her daily life and behavior have been similarly scripted by her thoughtless obsession with the shows and her inattention to her real family: Montag.