Controlling separate heat and AC devices from a single thermostat
This shouldn't be a problem, as long as you get a thermostat that supports separate heating and cooling power supplies.  Any thermostat with both R, and Rc, and/or Rh should be able to handle what you want.
R   = power (usually 24 VAC).
Rh = power from heating system.
Rc = power from cooling system.
The purpose of the separate Rh and Rc terminals, is so that the heating and cooling systems can each have their own separate transformer.  In some cases there is only one transformer, so the Rc, Rh, and R are all connected together.  When separate heating and cooling systems are used, Rc should come from the cooling system, and Rh should come from the heating system. Y Would be the cool call back to the cooling system, and W would be the heat call back to the heating system.
Installation
Pull 18/4 or 16/4 cable from the thermostat to the heater, and the same cable from the thermostat to the cooling system.
Cooling

Connect the red wire to the R terminal at the cooling system, and the Rc terminal on the thermostat.
Connect the white wire to the Y terminal at the cooling system, and the Y terminal on the thermostat.
(optional) Connect the green wire to the G terminal at the cooling system, and the G terminal on the thermostat.
Leave the black or blue wire disconnected.

Heating

Connect the red wire to the R terminal at the cooling system, and the Rh terminal on the thermostat.
Connect the white wire to the W terminal at the cooling system, and the W terminal on the thermostat.
(optional) Connect the green wire to the G terminal at the cooling system, and the G terminal on the thermostat.
Leave the black or blue wire disconnected.