I'm not sure about the headset vs. hands free. However, the TCH's connection is Bluetooth. By it's very definition Bluetooth is monogamous, meaning it can only connect to one device at a time. Once the phone and car are connected the phone cannot connect to another Bluetooth device (e.g. an earpiece) until it disconnects from the car. Likewise the TCH will not connect to another phone until the link between it and the current phone is disconnected.

It's not a limitation of the TCH. It's the way Bluetooth is designed to work.