I haven't used that particular AprilAire. Look in the documentation for instructions about tying the two systems together. Just about any T-Stat allows this. I can't imagine why you'd need to do this, but in the worst case you'd need to add a relay to isolate the two systems. Most heating and cooling systems expect a simple contact closure for control. On the air conditioning side there may be a separate Fan circuit for a total of three contact closures. Heat pump systems may have additional circuits for the emergency electric heat.

The worst part of this adventure is figuring out the color codes. It's best if you first forget any color codes that you presently know. (and keep your fingers crossed that the original installer used the correct codes.)