In Bradbury's Fahrenheit 451, Mildred refers to the people in the programs she watches on the parlor walls as her "family."
Montag notes that it was he that first started referring to the characters as members of the family, we can assume, because of Mildred's preoccupation with them. He started to refer to them as aunts and uncles, as if they were people Mildred really knew. It is safe to assume that Montag has never seen them as anything more than images on the wall. He has been unable to find anything of merit in watching the programs.
In "The Sieve and the Sand," Montag is trying to get Mildred interested in the books he has smuggled home. He is trying to make sense of the world he has only just now become aware of with Clarisse McClellan's help. Mildred could not care less about the books. She states:
Books aren't people. You read and I look all around, but there isn't anybody!
Conversely, Montag looks at the parlor walls and sees nothing. Things seem to happen with the sounds and dialogue, but nothing really takes place at all. For Montag, the characters on the wall are empty and meaningless.
Now...My "family" is people. They tell me things: I laugh, they laugh! [...] And besides, if Captain Beatty knew about those books...He might come and burn the house and the "family." That's awful! Think of our investment. Why should I read? What for?
Several pages later, Montag asks:
Does your "family" love you, love you very much, love you with all their heart and soul, Millie?
Why'd you ask a silly question like that?
It would appear that relationships are not what matters to Mildred. A relationship requires interaction between two people. However, the parlor walls are simply another distraction in this society to entertain and allow the inhabitants to ignore things that really matter in the world. Mildred does not worry about the woman who set her house, books and self on fire. She is not distressed about Clarisse McClellan's death. The only thing she really cares about is the continuation of her life undisturbed by unpleasantness and any need to think at all.
If Mildred's "family" is made up of the fictitious people on the parlor walls, we can assume that she has lost her connection with her husband. She has no connection with any living person that does not sit and watch the parlor walls with her, but even those associations are based on mindless entertainment.
In that family really is not important to her, and the things she cares for most are not real, we can infer that Mildred's character is extremely shallow. She only cares about being permanently numb. She does not care for others. If her house is burned down, she worries over the loss of their investment in the three parlor walls. In fact, early on in the story, all Mildred talks about is getting a fourth wall, despite the fact that they are very expensive.
Mildred is as superficial as are the many forms of entertainment society provides to close people's minds to questions and original thought. Mildred has become mentally malleable: she does not want to think for herself. She allows society to shape her perceptions and her truths. Mildred is nothing more than a puppet who cares only about living in the mindless state the government has created and reinforces daily by force.
Character is generally defined as a "moral or ethical quality." It is knowing the difference between right and wrong, choosing to do the right thing and caring for other people and world. It implies a concern for people and things beyond oneself. Mildred is not interested in any of this.