why his sister and not her sister? with what word possessive pronoun is matched?
Most of the Hindi words are pronounced like they are written but the ह is the letter that defies this rule most of the time. Whenever it comes in the middle or at the end, it changes the sound.
Colloquially, most people barely ever bother to pronounce ह when it is not at the beginning of a word. I personally blend बहन so it sounds more भेन.