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Your old thermostat is a 'communicating" thermostat designed especially for your system.The Honeywell is a conventional thermostat.
It may be possible to convert to a conventional stat but you will lose the communicating features.
If you definitely want to change over, look in your units and see if there are lettered terminals on boards along with the numbered terminals.
If so you will need to run extra wires between units and thermostat unless you already have unused wires.You will need at least 6 wires for the conventional stat and they will match terminals in units to letters on thermostat.
If this is something you really want to do, give me model on indoor and outdoor units and I will be happy to guide you.