You can use any heat/cool thermostat on the market to do this. All is required that you run 2 separate 18/4 wires from each system to the thermostat.
R is what carries continuous 24v power to the thermostat. RH is continuous power for heating, and RC is contentious power for cooling. As long as you have constant 24v to these terminals, your system will work. Many modern thermostats have these built in to one terminal on the thermostats (will only show R). All the thermostat does is split the 24v continuous power to RC and RH at there thermostats control board.
From Furnace:
Connect R to R - If your thermostat has RH and RC you can either keep the jumper in, or attach it to just RH for heating. This does not matter as long as you have 24v constant from the unit.
Connect W to W For Heating
Connect G to G for the Fan
From A/c Air handler:
Connect R to R - you can use both R wires at same connection on thermostat if there is only an R terminal. If there is RH and RC like above, you can either leave the jumper in, or connect it to RC.
Connect Y to Y for Cooling
Connect G to G for the Fan
The reason for connecting the G terminal for only the air handler is because you will only really want to have the fan continuously running for the cooling season. Additionally, depending on the type of air handler you have, some control boards require the Y and G terminals to be energized together to run the Cooling and the Fan speed on high. If older units with older style control boards have just Y energized on a call for cooling, the unit will only run the outdoor condenser, which will cause issues with the system. Almost all thermostats will energize G and Y together to avoid this happening if there thermostat is used on a older system.