I talked with my manager and he assured me that inter-airline rules do specify that you would pay both sets of fees, but I think you can rely on sbm12's practical experience here and guess that you would be only charged one set. The problem (or the fortunate thing, in other words) is that this occurrence is so rare, many check-in agents don't know the appropriate rules and simply treat it the same way they would a single ticket interline. You can encourage this behavior by synthesizing a single/seamless itinerary to show them.