Christopher's view of his father is rather innocent and immature at the beginning of the novel. However, after Christopher's discovery about the death of the dog and that it was his own father that killed the dog, his view of his father changes. The relationship is further damaged by the fact that Christopher discovers letters addressed to him from his mother, whom he'd been told was dead. This prompts him to leave his father and search out his mother. In the end, his father attempts to mend the relationship and we are left believing that they will mend the relationship, but that the innocent trust and belief of a son in a father, is gone.
As far as his mother is concerned, he's never really known her, but still she is ready to give up everything, including her country(she's living in London at the time) to move back to the US with Christopher. She seems very ready to step into the mother role. However, as Christopher has not had any experience with having a mother, the relationship does not seem to go beyond a certain depth.