I have a similar issue: If the A/C is on when I turn the headlights, on the A/C cuts out and the heat comes on. At one time, turning the rear defogger on would stop this, but now the rear defogger won't come on with the lights on to "bypass" this bizarre arrangement.
I have a 2004 Jeep Grand Cherokee with dual control HVAC which seems to be possessed. The problem started on a hot summer day when the AC abruptly stopped working and HOT air started to blow. Next we were only able to get really HOT air or really COLD. It's now become somewhat random with, for example, a setting of 69 degrees producing COLD air and 70 degrees producing HOT air, plus one side of the car, even though the settings are identical, will blow cold and the other hot. Our mechinic (as shown on his work tickets) originally replaced the thermostat, then he replaced the "air doors and actuator", now he has replaced the "AC Control Module". I believe he has also changed out the Control Module a second time suspecting that the first replacement was defective. While he's not a mechanic at a Jeep Dealership I believe he's competent and honest, for much of the work he has not charged us. He seems to be honestly stumped. When we have called the dealership to ask if this is a common problem, their response is "no, we're not familiar with that type of problem" and they recommend that we bring the Jeep in for service. Is this an unusual problem and what solution might I suggest that our mechanic pursue? Any help would be appreciated.