After David's mother died, he was left with his father and his aunt. David's father would often come home drunk and, as David grew older, he realized that his father would often spend nights with various women. For reasons that he did not understand, David despised his father for his behavior.
David's father wants the two of them to be like buddies. Yet David says, "I wanted the merciful distance of father and son, which would have permitted me to love him" (1.1.54). After David gets into a drunk driving accident, the two of them open up to one another. David begins crying and his father admits that perhaps everything was his fault. Though it would seem like a watershed moment, David knows that something had changed and that now they can never talk to one another again.
After David leaves for Paris, his father largely disappears from the story. At one point, Giovanni asks David to demand his father send him money, but David doesn't. Shortly before Hella arrives, he receives a letter from his father that makes it clear that his father doesn't understand why he's in Paris and wants him to come home. David thinks that his father really wants to ask him if he is staying for a girl, but he can't because he is afraid David would say no.
After Hella accepts David's marriage proposal, David writes his father a letter to tell him that he is coming home with a bride and that they will all be very happy.
It is clear that David's relationship with his father shaped a number of the neuroses that he experiences in later life, and that he is constantly trying to live up to his father's expectations, even when he doesn't know what those expectations are. His father's constant desire to be completely open with his son actually leads to distance between them, because there are certain things that David either cannot or will not explain to him.