(take this with a grain of salt, I've never flown a helicopter, closely examined a helicopter, or shot at a helicopter).
I have to imagine the first question is 'what sort of a helicopter?' The bigger the helicopter, the more body there is that's irrelevant to its actual functioning, and the more mass it has to get through to reach the good bits.
Since you brought up a Huey, let's take that example. From what I understand, the majority of the Huey is not especially impervious to bullets, at least not significantly more than a good, Detroit-made car (which, as box of truth has shown us, isn't very much). However, the helicopter will continue to work as long as the engine and control surfaces are still functional, which seem to take up a very small part of the entire vehicle, and as long as the pilot is still guiding it. I don't know how big the gas tanks are on a huey, so that could be an option as well.
Because of the nature of angles, and the fact that most of the good stuff is on the top of the vehicle, a shooter on the ground is more likely to hit the bottom of the vehicle and the bullet passes all the way through without hitting anything vital. So for average shooters on the ground who are just shooting for the main body of the helicopter, they could probably shoot all day long and as long as they don't hit the pilot, they're unlikely to hit anything of import. Of course, the shallower the angle, the less likely they are to hit anything, but very few people are able to shoot straight up or down, so most people will be shooting at an angle.
I have to assume if you're shooting from above, you're fairly likely to hit something, since if you're aiming at the center of mass, you're aiming at the engine, and any misses run a risk of hitting the rotors (keep in mind that, with the speed that bullets move, most shots through the plane the rotors spin are very unlikely to actually hit a rotor).
Should a helicopter get hit such that the engine stops operating, it should still maintain a slight gyroscopic effect. I don't know if that will be sufficient to land the vehicle, but it will prevent it from simply falling to the ground (obviously, if the rotors fall off, that's a different matter). This is an interesting difference from airplanes however which, even when out of fuel, can glide a long way and safely land, since helicopters are so energy intensive.
Also keep in mind, tactically, helicopters are unlikely to come close enough for engagement with small arms. From what I understand, medical helicopters are unlikely to enter a hot zone until it's been sufficiently secured, and any combat helicopter is going to stay far away and use its superior firepower to shoot you well before you can even see it.
