Are you comfortable with who(m) he is?

Solution 1:

Whom would be wrong in your example; it should be who. The reason is that a relative pronoun functions as part of the relative clause, not of the main clause. Don't let the question mark fool you: who is a relative pronoun here, not an interrogative one.

Are you comfortable with [the person] who he is?

This shows the structure of your sentence a little better. The person, the hypothetical antecedent of the relative clause who he is, is left out or enclosed in the relative pronoun who. In any case, who is part of the relative clause, not the main clause. That is why we should be looking at its function within the subordinate clause: it is subject (or subject complement) in who he is; therefore we need who, not whom.

It does not matter at all what function the (explicit or implicit) antecedent has in the main clause:

I fear him who gave me life.

I fear him whom I have wronged.

He who gave me life frightens me.

He whom I have wronged frightens me.

If who/whom is used as an interrogative pronoun, i.e. not introducing a subordinate clause, it is its function in the main clause that matters:

Who are you?

Whom do you see?

Note that who is now more frequent than whom in any case, and is accepted by most wherever traditionalists would have whom as explained above.

Solution 2:

“Who he is” is just a noun phrase. As such, it cannot take any further inflection, no matter whether it’s included as a subclause:

Are you comfortable with who he is?
Are you comfortable with him?

You are comfortable with who he is.
You are comfortable with him.

Just like a phrase with whom, such as “whom he loves”, doesn’t change in the same context:

Are you comfortable with whom he loves?
Are you comfortable with her?

You are comfortable with whom he loves.
You are comfortable with her.

Use of who or whom is entirely dependent on the contents of the clause, not the phrase in which the clause appears.