Not elegantly... I think you could both choose "solo mode" in the Battle Interface to have access to all 4 characters, but only one of your can be the Black (Game Master) color to see all the cards in the player's hands. If one of you chooses White (Player 2), you could just dump player 1's cards on to the table off to the left (or Player 4 off to the right).

Set up a four-player game, and swap between player colors to switch characters. I play two characters in my three-person game like that, and it works quite well.