So here is the backbone of the Maritime Navy, the Dauntless-class frigate:
One issue I see is that you've got your light forces using US type missile systems (ESSM), but your blue water forces using European systems (ASTER). While it's certainly possible for a nation to use both it introduces logistical complications, so outside specific cases is avoided.
Those specific cases?
While transitioning from one generation of systems to the next (e.g. Italy or France as the first ASTER equipped ships came into service... but ESSM and ASTER are the same generation...)
For internal political reasons (two services treading on each others toes)
For external political reasons (e.g. Finland's Cold War era purchasing policy)
For security of supply (so you don't get crippled by one nation cutting you off e.g. Israel before they got the yanks firmly on side)
Because you picked up a bunch of cheap second-hand warships (e.g. the Chilean Navy... Barak, Sea Sparrow, Standard I and Sea Wolf!)
So, there's nothing wrong with it, but you probably should include some justification in the history/politics posts (e.g. ill-will between the Coast Guard and Navy; the Corvette's ESSM isn't really ESSM but a new home-built missile which looks similar; etc.).
Also, on the Corvette/Cutter... particularly in the Cutter role I'd be strongly tempted to swap the Phalanx CIWS out for a 57mm instead. With appropriate ammo it's just as good or possible better in the CIWS role, and it's longer range make it more suitable for popping warning shots across the bows of stray fishing vessels.