When Christopher's father first appears, he is collecting Christopher from the police station. Christopher says:
Father was standing in the corridor. He held up his right hand and spread his fingers out in a fan. I held up my left hand and spread my fingers out in a fan and we made our fingers and thumbs touch each other. We do this because sometimes Father wants to give me a hug, but I do not like hugging people so we do this instead, and it means that he loves me.
This shows the bond of trust between father and son through the secret sign they have to show love, without the physical contact that Christopher dislikes.
Later in the novel, it becomes clear that Christopher's father is keeping at least two great secrets from Christopher (what happened to Wellington, and what happened to his mother). However, it is also evident that this is the exception rather than the rule. For instance, Christopher's father understands how important it is for his son to take his mathematic A-level and refuses to discuss the matter behind his back:
Then Mrs. Gascoyne said that she and Father should talk about this at some later point on their own. But Father asked her whether she wanted to say things she was embarrassed to say in front of me, and she said no, so he said, “Say them now, then.”
Immediately before he confesses to killing Wellington, Christopher's father tries hard to be completely honest with his unreceptive teenage son. He attempts to draw a distinction between being generally trustworthy and being perfectly truthful all the time. In doing this, he is trusting his son as well as asking for trust:
Then he said, “Look, maybe I shouldn’t say this, but … I want you to know that you can trust me. And … OK, maybe I don’t tell the truth all the time. God knows, I try, Christopher, God knows I do, but … Life is difficult, you know. It’s bloody hard telling the truth all the time. Sometimes it’s impossible. And I want you to know that I’m trying, I really am. And perhaps this is not a very good time to say this, and I know you’re not going to like it, but … You have to know that I am going to tell you the truth from now on. About everything. Because … if you don’t tell the truth now, then later on … later on it hurts even more.”
Although this is unsuccessful in the short term, by the end of the book, it appears at least possible that Christopher may come to trust his father again.