A documentary interview is about the relationship between the filmmaker & the subject.
I once mentioned this to a colleague and he said,
"Yeah, but you mean, like, intellectually, right?"
It's a perceivable quality in the movie.
Look at any Errol Morris film to see what I'm talking about.
His movies are not just about the subjects, whom anybody has access to (in theory): they're about the interplay between himself and the subject - and the environment Morris sets up to capture that kind of interview.
A good first step in achieving this effect is simply doing your research.
I did an interview with a teacher-entrepreneur for a promotional film.
While doing my initial research, I discovered he had quite a popular TED lecture.
So I watched it, and took special note of the things he said - especially the little things that we possibly had in common, in order to build rapport later on.
Flash forward to the interview.
Our client told us that he's very serious and normally does not consent to interviews.
We expected this to be a difficult experience.
While the cinematographer was setting up, the subject asked me, "Am I shiny?"
Remembering how he mentioned in the TED lecture that, as a young man, he took a sabbatical to India to find himself, I responded, "Only on the inside."
A big smile swept across his face.
"This guy's going places," he told his assistant.
And the interview he gave was brilliant.