I just started a little mod to learn the editing features and i'm already stuck with this plane problem. I tried many different solutions, and i have to confirm that the ones explained in this thread are the only working ones, even with C3C.
You can make them land units, and bypass the ocean limitations with the rebase option or, the best in my opinion, is to use the invisibility, and leave them Air.
In case of helicopters, as just been said, makin them land units with no terrain limits gives you a realistic output. Helicopters will not be able, then, to attack far sea units, but this is not a problem, it is just as it should be.
But your fighters will need to attack ships, and since the editor don't let you build mixed units (a BIG flaw in my opinion), you just have to hope that there will not be too many units with the chance to spot the invisible airplane.
As long as you are making "normal" fighters or bombers, when sometimes you fall in radar range, and the plane is taken out by a common ground unit, this is not a total nonsense. Since the only units able to spot submarines are modern ships and a couple of hi-tech ground little bastards, you can always think of a bad ground to air missile attack, 'cause there SHOULD be a nearby strong unit or installation.
This don't work always, of course. I was taken down a couple of times by ancient units while testing in debug mode. I'm not sure if this happen 'cause the AI "cheats", and let his horsemen see the invisibile plane, or if it's just bad luck, when the ground unit chose to step right in the square where you are "hiding".
For massively customized mods, i can only suggest to be really careful when adding the ability to spot submarines to any custom unit. As i see by now, with a near-original mod with just a unit edited with this air/invisible trick, things goes quite well, and even the AI seems to use them decently. I don't know what would happen with a more complex mod, but nothing good i fear...