Actually most people no longer use an invert switch. The switch is useless when you are flipping over repeatedly and such. We use a combination of throttle and pitch curves programmed into the radio so that you have full throttle at the top and bottom of the stick and postive pitch at the top of the stick and negative pitch at the bottom. Basically when you roll inverted you just pull the throttle stick back to what you would usually associate with idle. There are multiple curves programmed into a heli radio generally and the 1 for inverted flight is usally called Idleup 1 or Stunt 1 with normal mode allowing only upright flight.

FWIW, most airplane radios do have the software to create the required throttle and pitch curves for helis. Some radios have it all though such as the 7, 8 and 9 channel radios from JR and Futaba, and some of the newer 6 channel radios so they can fly planes and helis.