I'm in the middle of that right now, except it's 3 ways, and it happens every time I see my oncologist.
Both my oncologist and the facility my oncologist works at bill my insurance, which sees two bills and are unable to correlate that the visits happened the same day, same time, and are the same visit. The facility's billing department won't talk to the oncologist's billing person, neither will talk to my insurance company, and my insurance company won't get the two of them on the phone at the same time. About half the time, I get stuck with two copays for the same visit, which amounts to $89. I fired my surgical oncologist because I just can't afford to go see both my chemo doc and the surgeon once a quarter, if it's going to result in that bullshit.