I did a bit more reading over lunch. In case someone else comes by this post, maybe it will help them. I'm not 100% sure of any of this - use at your own risk. Please let me know if I'm way off base.
I think this is the spec sheet (please let me know if you disagree): http://www.hongfa.com/pro/pdf/HF3FF_en.pdf
There are 2 ways this relay can be wired up. Form A and form C.
Form A is like a light switch. Power comes to the switch, if it is thrown to the on position, it completes the circuit. It is also called SPST (Single Pole, Single Throw).
Form C is more like a light switch that toggles between 2 lights. One light is always on, the switch picks the light. These are also called SPDT (Single Pole, Double Throw).
I'm guessing here, but I'm guessing that this relay is using SPST, or Form A. Heating and cooling each have a relay that is normally off. They each get activated independently. So, if my spec sheet is correct, the max current is 15A in this mode.