possessives - When can two pronouns being compared in a sentence be of different types?

I came across a sentence today -

He resents your being more popular than he is

I always thought that while comparing two pronouns they should always be of the same type, like,

She is taller than he (is)

or

I care for him more than her

I understand that the first sentence that I mentioned is correct but the moment you take out the is in the end, my perception begins to change.

He resents your being more popular than he doesn't sound right to my ears.

Shouldn't this sentence, then, be -

He resents your being more popular than his

What rule is being followed here?

Edit: The question that this one has been marked as a possible duplicate of pertains to gerunds and the usage of possessive pronouns with them while my question is regarding comparison between two possessive pronouns in a sentence. Only the sentence used as example in both the questions is same but the questions asked are entirely different.