***** NOT A TEACHER *****
(1) It might be easier to analyze if we add a few words:
I have been married for ten years.
(2) In my 1988 edition of Longman English Grammar, it says
that "Some participles used as adjectives[my emphasis]
combine with have/had been":
My uncle has been retired for more than five years.
She's been gone for half an hour.
(3) I think, therefore, that we can conclude that your sentence is
NOT a passive sentence. It describes a state, not an action.
(4) That book also says that if a participle is used as an adjective,
it cannot be used wth by + an agent. In other words, you cannot
say "I have been married for ten years by the priest."