what his life has been like is idiomatic. It is how a native speaker might refer to another person's ups and downs, challenges, successes, failures, health, family, job situation, and so on.
I asked him what his life had been like.
I asked him how he had been.
I asked him how his life had been.
All three are perfectly grammatical. To my ear, however, asking someone "what their life has been like" suggests more probing sorts of questions or a wider range of questions than is implied by "how his life had been". The former wants details whereas a person asking "How has your life been?" might be content to receive "I've been doing quite well" as an answer. They both refer to life, which is broad in scope; the nuance is carried by like.
But many speakers might hear no such nuance in like and treat it as a throwaway word, and they might hear these examples as nearly identical:
I hear you took a road trip from Florida to Oregon. Tell me what it was like.
I hear you took a road trip from Florida to Oregon. Tell me how it was.
I hear you've been to their production of The Tempest. What was it like?
I hear you've been to their production of The Tempest. How was it?