When we first met he made a lot of noise about big expeditions in remote areas and alpine climbing, therefore I understood that he had enough climbing experience not only to climb outside but also to lead some stuff.
Just because the guy climbed on a few expeditions doesn't mean that he has technical skill or can lead climb. You should not have assumed that.
This is not a difficult problem to solve. Ask some simple questions before your trip and then agree on what each of your roles will be during your climb.
-Can you lead climb?
-What have you lead? (And do you have the sunburn to prove it?)
-I expect us to alternate the lead during our climb. Are you up for that?