Navy doesn't seem that strange. I mean, they're referred to as ships, with all the different ship parts on them like bow and stern, port, starboard, etc. and they basically manoeuvre like boats, just with an added dimension of movement.
In addition, in the faction feature for the Mercantile Guild, it explicitly states that the Guild has a considerable naval force, used to patrol aerial trade routes.
So there you have it, airships are considered part of the navy. The only trouble is differentiating between airships and seaships. Do they call both "the navy"? do the factions each even have a sea navy? So many questions, so little answers...