I do not know the actual IATA rules, but your contract is generally with the initial carrier. Your ticket (or receipt, printed on IATA ticket stock) will read who issued the ticket in the upper left corner. It would seem (and who knows the laws elsewhere) that in the US, you have a direct contractual relationship with the issuing carrier. It is the "issuing" carrier on a multi-airline itinerary that collects all the $ and distributes it accordingly (ie, travel agent commissions, interline airline portion, etc.) You have no contract with the secondary carrier.

Having said all that, who knows. I don't have a good answer. There are probably some explicit IATA regulations on point. But as your "final destination" carrier is probably the only one that has a baggage service when you get to your final destination, it would have some sort of agency relationship with the first (issuing, contractual) carrier.