Why does my husband get frustrated so easily?

My husband is a super sweet guy, very generous, and kind of a doormat. He's always polite to strangers and you can get just about anything from him just by asking. If you met him, you'd never think that he would even be capable of getting angry, let alone throw and punch objects in rage, or yell at me, his wife, over small inconveniences.

However, living at home with him, just the two of us, I've noticed and unfortunately experience his frustration first hand. We'll be playing a game together on the computer or working on dinner or a home improvement project and he'll slowly start to become more and more snappy, and by the end of it, he'll be shouting and slamming doors over nothing at all. We've talked about it a lot and he honestly can't tell me why he's so upset most of the time. When he can find a reason, it's always something small and insignificant and that knowledge tends to upset him more.

We both agree that his anger isn't right, that it isn't him or who he wants to be, and that something needs to be done about it. Being in the military however, he's had bad experiences with psychs not being very helpful, and also is afraid that if he is prescribed certain drugs he'll be kicked out altogether. Suffering from severe depression and anxiety myself, I know that psychs CAN be life savers, but I understand his concern and I don't want him to lose his job.

What can we do?