I've always been of the opinion they were part military. All you have to do is watch the battle scenes during the Dominion War, there were a lot of ships there that were built for exploration armed to the teeth & fighting. They're primary mission may be exploration but there is at least some military part to the job.

Starfleet is a military, with a wide ranging set of mission parameters. Sometimes that's "exploration/research/science", other times it's balls-to-the-floor attack scenarios. Neither means it isn't a military. There's no such thing as a 'part-military'. 