First, read my explanation about the roles of Rosenstein and Sessions:
Muellers is not as clear to me. He is definitely a Black hat under duress acting as a Black hat on order from White hats.
I think his main role is to investigate the Deep State but acting as if he investigates Trump. This can be seen in the Manafort trial (Manafort is Deep State, partner with Podesta and ties to the Clintons), where Mueller got him convicted.