HID's use high voltage to power the light. To convert DC voltages up to a higher voltage, you either have to turn it into AC via an inverter, or you have to use a switching circuit to basically do the same thing.
This method, if not done right, can and will create a lot of RF noise. Improper shielding, poor design, etc will all make this worse.
I'd bet you coffee and a donut that if you take the HID lights off and put the standard lamps back in, all your problems will go away, well at least the radio problems.
You could also try moving your power feed to your radios away from the HID ballasts, and make sure your radios are fed directly off the battery, and not another circuit somewhere. These noise issues are one of the reasons why installers will always make a direct run to the battery and pull power from there.