Character Breakfast I believe is available at Cafe Mickeys, but others know more about that than me.
As for Character lunch, I can recommend Auberge de Cendrillon if you are interested in the Disney princesses.

It's very expensive though, the food is great, but that price is quite the turn-off for many.
It's €65,99 for adults and €36,00 for children.
Inventions doesn't have a Character lunch I believe, only dinner, however there is the Themed Character Brunch on Sunday.