An interesting part of the novel to look at in response to this question is in Chapter Fifteen, after Holden has made a date to see Sally. He talks about his parents and he mentions that he believes his father is quite wealthy because he is a corporate lawyer and he is always investing money in Broadway shows that turn out to be a big flop and he makes a loss. Note what he says about his mother at this stage:
They always flop, though, and it drives my mother crazy when he does it. She hasn't felt too healthy since my brother Allie died. She's very nervous. That's another reason why I hated like hell for her to know I got the axe again.
Note the concern that Holden shows towards his mother. It is clear that he cares for her a great deal. He mentions her poor health and the way that she is very nervous, and he hates the way he knows that it is going to upset her even more to here that he has been expelled from yet another school. So, I think we can make an argument from the text to indicate that Holden does love his mother deeply. We are told less about his relationship with his father, except for the way that Phoebe repeats, again and again, that Holden's father is going to "kill" Holden for getting expelled. Both parents obviously love their son and are concerned for him, although it is clear that Holden feels more strongly about his mother than his father.