There are some quests that require two heroes to play. One is the main hero and the other sort of a helper. If you have this kind of quest you'll have two face icons showing and can click either one to give them things to do. I found it easier if they weren't on the same time schedule, so one could be asleep while the other did their part of the quest. Other than that, you don't switch your characters. It's just not possible to do as far as I know.