"Is there a reason why someone would install two firstco hbxb-hw & Mbxb-hw coil units with heat capability to cool a one story house? "

Maybe because the house is cold but if you nor the installer know's,I doubt anyone else does.

If I read that correctly, it's a heat pump which is essentially an air conditioner that can be ran in reverse to heat your home. If you did not already know this. The compressing unit costs a bit more because of the reversing valve and defroster. You can tell them to put a straight AC unit in or just go with it. It can be a secondary heat source if you primary goes down for any reason. Your original question though, I agree with Klem1 if neither of you know why, it is unlikely any of us will.

As Kevin said, a heat pump is an air conditioner in reverse. It removes heat from cold outside air and puts that heat into your house. This takes less energy then creating the heat, so a heat pump is a more efficient way to heat your house, as long as it isn't too cold outside (some heat pumps work down to -30° F). So you can use in conjunction with your radiant heat and save some money.