(while not literally being Batman/Indy games)*
I actually read that after I posted but I didn't feel like editing the post after I did the work and research of typing that all out there.
I guess a few suggestions that would be more what he is looking for:
Tomb Raider <---- obviously a female Indiana Jones if there ever was one.
Pitfall, Super Pitfall, and every other Pitfall game <------ all obviously similar to Indiana Jones in many respects.
Castlevania <---- because the hero uses a whip which makes him like Indiana Jones, and maybe also a little bit like Batman as well.
Prince of Persia <---- the developer of this game even said (according to Wikipedia) that some of the inspiration came from the Raiders of the Lost Ark.