Singing Through My Diaphragm?

I have a vocal coach, and forgot to ask this, for some unknown reason! Anyway, when I am breathing through my diaphragm, my stomach goes out, and when I exhale, it goes in. Now my question will make me seem a bit uneducated, but forgive me for that! When I inhale, do I inhale through my nose, or my mouth? It just occurred to me that I could be breathing wrong because I have been inhaling through my nose. I really would like to sing! I am not that good, but I am working on it, very hard. Is it possible?