I'm trying to help my neighbor (single mother of 2). I am fairly knowledgeable of electricity flow, voltage, capacitors, relays and such. She has an American standard HVAC. Her AC works fine. However when the heat is turned on after a few minutes the A/C also kicks on and trips her circuit breaker. I checked for burnt/loose/coroded wires. The breaker doesn't get hot. I don't know a lot about HVAC units and not sure that both should kick on or not (seems a little odd to me, to be a able to heat that the AC turn on).

She has a heat pump.
Two main things to look at.
1. capacitor; if it looks bad; swollen, leaking then it needs replaced. Some meters have a test setting for capacitors. Check the capacitor or just replace it. Its usually under $20.00.
2. a bad compressor; easy to check. Look it up on YouTube for step by step directions.
Make sure you kill power to the outdoor unit as well as flip the light switch next to the inside unit.

I just re read your question. The A/C works fine? Then scratch what I said. It's a bad valve inside. Need a technician to look.

What type of heat is it? Does ac ever shut off?

Need to find out if this is a heat pump system ? If not there is a chance you have a low voltage problem . Has any one changed the thermostat ;i.e. electric to a heat pump stat. Look inside the out door unit for a reversing valve; it will have 4 pipes going to it, one @ bottom, 3 @ the top .