He stole a car. That's completely out of character for him.
My dog bit a child yesterday. It was a shock as that's so out of character for him!
"In character" is used more when talking about actors. If someone is "in character" it means they are behaving, speaking, moving etc exactly as the character that they are playing would. With method acting, the actor would even continue to be "in character" during breaks from rehearsing, filming and even when at home for the duration of the play or film.