Atticus trusts Jem and Scout so much not because of who they are, but because of who he is. He trusts them so much because that is his way of making them into adults, his way of raising them to be good people.
Atticus, like any parent, wants his kids to grow up to have good values and be good people. Some parents think that the way to do this is to keep strict control over their children, but that is not who Atticus is. He wants his children to think and he wants them to do what is right because it is right (like he does) not because they have to.
Atticus feels that the best way to do this, the best way to make them into adults, is to treat them like adults. Because of this, he treats them as if he trusts them even though he knows they will make mistakes from time to time.