Fred had a good relationship with both her parents, didn't she? (I realize that may be the lone example in all of Joss' work. Though I don't think we heard much about anyone's parents on Firefly, other than the Tams'.)
Jayne and Kaylee seemed to have good relationships with their parents, but they were only mentioned a couple times. Bad relationships are more interesting. Joss's writing overall became less interesting to me after he had his first kid and all the stories had to have a kid or a family in them. Even in Firefly, if it had continued, Wash and Zoe would've had a baby. Although Darla's pregnancy storyline was one of the best ever, and made her a far more interesting character than she'd been before (and she was pretty interesting before). That was the only time I've ever been super-invested in a fictional pregnancy. Unfortunately, after the baby was born, Angel became nearly unbearable.