As I understand it お父さん is the usual way to refer to someone else's father in everyday speech.
What about when you are writing a formal discussion (for an academic audience) of an interview you had with someone? Is 父 or 父親 better for this?
Japanese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Japanese language. It only takes a minute to sign up.Sign up to join this community
I would suggest the exact opposite, when writing especially for an academic audience you should minimize the amount of 敬語 as there specific styling for just that use case (である/だ vs. です)
according to a tertiary search on Google, it seems just using 父 and 母 is best.
I would take no risk, and go with お父様.
In my understanding, 父親 is more like the generic word for father. From http://jisho.org:
A father (or dad) is defined as a male parent or Individual progenitor of human offspring.