I purchased two separate tickets from DFW-DEL then DEL-KTM (round trip) . I purchased my tickets through travel agent. I was advised that as far as I am booked on same reservation, airlines will checked the baggage until final destination.For returning also same rules will be applied. I did the same. I had no issues with luggage. It was through check-in while going and coming back,hassle free.

As far as it will be on same reservation, you don't need to check your baggage again.But you have to remind them at check-in counter.