What does Holden say about his mother and father in The Catcher in the Rye?

Holden Caulfield describes his mother as a hysterical woman who is extremely anxious and nervous all the time. She is still struggling to heal from the tragic death of her youngest son, Allie, and Holden sympathizes with her. He also says that feels bad for his mother after he drops out of Pencey and roams the lonely streets of New York City by himself.
Holden is not particularly close to his mother, which is revealed by the fact that she did not know that he wanted racing skates for Christmas or that he was infatuated with Jane Gallagher. He also mentions that his mother is a chain smoker and stays up smoking in the middle of the night. He says that his mother has a good sense of fashion and dresses Phoebe well. She is also a concerned parent who would cry and beg Holden to come back home if he ever ran away.
Holden describes his father as a touchy individual who wishes that he would attend Yale or Princeton later in life. Holden also mentions that his father is a wealthy, successful corporate lawyer. He invests his money into shows on Broadway but seems to have bad luck. Holden's father is a former Catholic and stopped going to mass after he married Holden’s mother. He is also a deep sleeper and would never wake up in the middle the night.
Overall, Holden has a strained relationship with his parents and is not very close to either of them. Holden's father seems to be more interested in his occupation, while his mother is struggling to accept Allie's tragic death.

It's fair to say that Holden has a less than ideal relationship with his parents, especially his mother. He describes Mrs. Caulfield in detailed terms as a very nervous, anxious woman. Permanently grief-stricken and beset by insomnia, she's finding it hard to get over Allie's death.
Although Holden doesn't get on very well with his mother, he nonetheless expresses guilt over adding to her worries by constantly getting kicked out of one school after another. He describes her initial reaction in such cases as hysterical but claims that she isn't so bad when she finally digests the bad news. Clearly, she's still preoccupied with the memory of her dead son.
As for Mr. Caulfield, Holden describes him with a degree of objectivity that indicates their emotional distance from one another. He tells us about how rich his old man is and what he does for a living. Holden vividly compares his dad's sleeping habits with those of Mrs. Caulfield:

You can hit my father over the head with a chair and he won't wake up, but my mother, all you have to do to my mother is cough somewhere in Siberia and she'll hear you. She's nervous as hell. Half the time she's up all night smoking cigarettes.

The implication here is that the death of Allie hasn't quite impacted Mr. Caulfield in the same way as his wife. The fact that he can sleep soundly at night speaks volumes.

Holden begins his story by describing his parents as private people who would be upset if they knew he disclosed anything about them; he claims they are "touchy about anything like that, especially my father."
When he decides to take some time alone before going home after his expulsion from Pencey, Holden clearly wants to avoid facing his parents. He says, "My mother gets very hysterical. She's not too bad after she gets something thoroughly digested, though." He understands that there will be a scene because he has to once again change schools.
Holden's family is wealthy; of his father, he says "My father's quite wealthy . . . he's a corporation lawyer." He describes his mother as "very nervous" in the aftermath of Allie's death. When Holden confides to Phoebe that he has left Pencey early, Phoebe tells him "Daddy s gonna kill you."
Holden does not share many of his parents' values. He doesn't enjoy urban living, and he rejects the idea of working like his father. He understands and empathizes with their concern for him, but he feels trapped by their expectations and their control over his life.