There is no such thing as two phase or split phase it is all single phase unless it is a 3 phase line coming in. The standard residential single phase power connection is about 240 volt coming in on 3 wires (red - black - white) the white wire is the neutral and is a center tap on the secondary of the transformer out on the power pole and all 120 volt circuits are connected to the neutral and either the black or red wire. The most common 240 volt 1 ph circuit is connected to the red and black wires and the third wire is a ground only that only has current flow during a fault situation.
You should not mix 120 volt and 240 volt circuits on one 240 volt circuit, use a separate 1 pole circuit breaker for your 120 volt circuits.