One example of Jem's innocence can be found in Chapter 7 following the sealing of the children's secret knothole. Jem naturally believed Nathan Radley when he told Jem that he was cementing the tree because it was diseased. After all, Boo's brother was an adult and should be trusted. However, Jem learned from Atticus that the tree was perfectly healthy, and Jem soon realized that he had been lied to. Jem saw that Nathan's true reason was simply to prevent Boo from making any further contact with the children.
He stood there until nightfall, and I waited for him. When we went in the house, I saw he had been crying; his face was dirty in the right places, but I thought it odd that I had not heard him. (Scout, Chapter 7)
Another example can be found when Jem discovers Atticus' marksmanship skills. Both children had come to the conclusion that Atticus was "feeble" with no special skills. Jem's discovery that "One-Shot" Finch was the best shot in the county opened his eyes to new possibilities of his father's character.
"I reckon if he'd wanted us to know it, he'da told us. If he was proud of it, he'da told us.
"Naw, Scout, it's something you wouldn't understand..." (Jem, Chapter 10)
I'm trying to find the same thing, actually. The only example I can find is at the beginning of chapter 22 when Jem cries because Tom Robinson was found guilty, even though everyone knows he was innocent. Jem was innocent enough to think that Tom had a chance of winning even though he is black and the Ewells' are white.
hope this helps a little:)