Before your interview, thoroughly research the budgetary constraints of the institution you are interviewing for and its budgetary outlook. Depending on the institution, they may have differing philosophies on the role an athletic director should play.
If taking part in some coaching, getting your hands dirty, and being an ear to your athletes' concerns and feelings is part of your philosophy, be sure to share that. If you find this useful in identifying the strengths and weaknesses of the program you are coming into, don't hold that back. However, if you find speaking directly with faculty and your coaches and examining the systems in place more useful, share that as well. Whatever your approach, try to align it as well as you can with what this institution has to work with while displaying your adaptability as a team player.