At Confusion this past weekend there was a panel on Zeppelins, especially as related to steam punk. The notion of blimp vs submarine came up as part of the discussion. I had remembered reading about such a battle occurring in World War II between a US Navy blimp and a German U-boat. It turns out there is only one recorded such battle:
Normally, U-boats would submerge at the sight of a blimp, but my understanding is that the U-boat in this action was damaged so that it could not submerge.
There were well over 100 US anti-submarine blimps produced in World War II. Each was armed with a 50 caliber machine gun and 4 depth charges.