Character cards are counted as cards in play along with ongoing, equipment, mechanical golem, and other non-one-shot hero cards. This question comes up with Miss Information's card "Explosion" in the Lab. That card says, "At the end of the villain turn, each player with 3 or more cards in play must destroy 1 of their cards." What it means in practice is that if you have 2 or more cards in play in addition to your character card, you must destroy one.