Some airlines do not cooperate, and so you must purchase two separate tickets.

If a consolidation site were to sell you two separate tickets from non-cooperating airlines on the same invoice, it would mislead buyers into thinking that they can expect a baggage transfer at the connection, and that if the first flight is delayed, then airline of the 2nd flight will be forgiving. I would not want to be the CSR at the receiving end of angry travelers who were mislead.

If you don't care about having two separate tickets, there are some consolidation sites that will at least compose the cheapest multi-booking itinerary for you, but I don't think you can ever get it all paid for on a single credit card charge. Check out the consolidation tools feature matrix to find out which sites support multi-booking itineraries.

Actually, cheap-o-air might give you what you want. Cheap-o-air will show you multi-booking itineraries (without telling you), and also sell you tickets. I wonder how many travelers buy a multi-booking ticket without even knowing.