Joseph is the biological father of David.
Joseph Strorm is a strict disciplinarian, and David knows this. Despite knowing that his dad is adamant about adhering to religious rules of Waknuk society, David still makes mistakes. Those mistakes really bring out the true nature of the relationship between David and his dad. For example, Joseph became enraged and accused David of blatantly calling upon the Devil to give him another hand. In reality all David was asking for was a little extra help.
"You — my own son — were calling upon the Devil to give you another hand!" he accused me.
"But I wasn't. I only —"
"Be quiet, boy. Everyone in this room heard you. You'll certainly make it no better by lying."
I don't believe there is much compassion and love within the relationship. Joseph treats his family in the exact same way that he treats the rest of the Waknuk people that he helps govern.
Despite having Joseph as a father, David grows up to be an incredibly patient and compassionate person. Perhaps it is because David sees how his father treats people, and David unconsciously decides that he will never be like that. I believe that is why David admires his Uncle Axel so much.
David's relationship with his father is a strictly ordered one. David's father is the Magistrate of Waknuk. This means that he is responsible fro enforcing all the laws pertaining to deviations and Blasphemies. He is a hard, unrelenting disciplinarian who zealously upholds the strictest command of the law. Since he is like this because of his character traits and his job, he treats David the same way.
He is demanding and harsh and gives David hard punishments when David crosses a line toward deviation or Blasphemy. However, something in David's relationship allows him to be a boy of independence and compassion and devotion and to grow up into being a courageous loving man. So David's relationship with his father is more complex than it may seem on the surface.