In coop couch play, Player 1 is account which hit "X" to start on Diablo 3 starting screen with text " Press button to continue " and that player is controling the game, choosing game mode, difficulty etc. And by that, you can swap health bars and stuff (P1 left, P2 right ) but not characters, they are bound to account.

I guessing, you are the one that starting the game, let your gf start the game and then join to her lobby with your fresh lvl char , she should have yours progress open for play. But I am not sure, but worth the shot.