I think the best example of respect between Atticus and his children is the basis for him taking the case, even though it should go to another lawyer.
Atticus tells Scout that if he didn't take the case and defend this man, he wouldn't be able to hold his head up in public nor would he be able to ask Jem and Scout to obey him. This is an important lesson he is teaching his kids. They must have respect and practice what they preach.
Another example of respect is later in the novel when Dill runs away from home and hides under Scout's bed. When Jem finds out, he has enough respect for Atticus, and that he will do the right thing, that he tells Atticus about Dill hiding under Scout's bed, though both Scout and Dill didn't want him to. This shows how much respect Jem has for his father. He knows Atticus won't turn Dill out. Instead, he will welcome him in and feed him and look out for Dill's best interests.
Atticus is not demonstrative towards his children but he wins their affection and respect.
He deals with them by reprimand rather than physical punishment. Jem tells Dill he has never "been licked" by Atticus, and that he was going to see to it that he never would be. When he chops up Mrs Dubose's flowers for bad-talking Atticus, it is Atticus himself who makes Jem pay her back with reading visits.
Atticus teaches his children to see things in a relative way and that adults are no more perfect than children. He explains to Scout why Miss Caroline reacted the way she did and why Mrs Dubose was courageous by defeating her addiction.
Atticus deals with his children through example as well. He remains polite to people when they are rude, even when insulted. He tells his children not to retaliate by fighting but to stand one's ground just the same. He explains to Scout that he couldn't hold his head up or tell his children ever again what to do if he didn't defend Tom Robinson in court. This concept might be over Scout's head, but he shows her that true respect is not automatic - it has to be earned.
The children see another side to their father when he shoots the rabid dog. They learn that Atticus was a "dead shot" in his day although he has never mentioned it. Jem sees that Atticus doesn't have to "strut his stuff" to be estimed and declares afterwards, "I'm a gentleman, just like Atticus!"
As a father and role model, Atticus is A-OK.