Did you book thru an online travel agent that put you on 2 unrelated airlines?
Please explain what you mean by "unrelated" - it is possible to sell a ticket for two airlines which aren't in the same alliance and still have them check through luggage - as long as there is an Interline agreement between the two carriers.
I did this a few years ago flying LAX to Berlin - first leg was Air New Zealand LAX to LHR [flight no longer offered] then LHR to Berlin on British Airways. Not a codeshare - not possible to book through BA or Air NZ, but available on Expedia - I used a local travel agent. Bags were checked through and it worked out fine - and it was actually an open jaw, with the return to LHR from Vienna.
But you do have to understand what you're buying - this may be different from the "two separate tickets sold together" that you'll see on Google Flights. It may be designated as "multiple airlines" - and you would have to recognize they aren't in the same alliance.