With different reservations/PNRs you are totally out of luck and on your own if you miss a connection/flight, even on the same airline.

Even if you buy a ticket from a place like Expedia or a travel agent that spans multiple airlines, the single PNR you receive is from the GDS. The individual legs on different airlines will be considered different reservations with different PNRs on each airline.

If you read through the forum, you will see several threads from people complaining about playing phone tag between a site like Travelocity/Expedia and two different airlines, because no-one is willing to accept responsibility for connections not part of that airline's reservation.