Why combine the two Crews though, would something have happened to this other Starship that would force that crew to go aboard Voyager? Voyager isn't a big ship and there really aren't that many that are smaller so if the other ship was like a Miranda or even a Nebula then it would be Voyagers crew that would have to transfer to those ships if anything happened as Voayger would be barely large enough to sustain any more than a dozen or so from either ship.
Anyway for the question the way I see it, depending on the scenario above then the Doctor would have to act as at least an Assistant to the Senior CMO, that is also that said Starship doesn't already have an EMH of there own and they could tranfer our Doctor to there ship should that scenario occur.