Not necessarily easy.

It all depends on the agent. Last November I had CO: IAH->AMS-> IAH and KLM: AMS->Vienna->AMS. Transfer between CO and KLM has to be one of the easier transfers. The Continental agent did not know how to check my bag through to Vienna. She asked another agent who proceeded to explain the long drawn out procedure and the risks involved. Since I travel light, I decided to carry-on my bag instead.