Well you can be depressed in the casual sense of the word - as in feeling very down or dispirited - when you fight. But that isn't the same as clinical depression. I can't find the DSM-IV definition of it but it's a sustained feeling of sadness for two weeks or more along with other symptoms including lack of energy, unintentional weight loss, irritability, thoughts of self-harm, etc. Personally I think the two week period is too short a time... and besides it usually drags on much longer anyway.

I think it is natural for you to be very upset by the arguments, even if they're not major ones. Perhaps you could try working on the causes of the arguments? Or what is actually said during the arguments, because maybe your husband feels the same way or similar...