A hybrid vehicle is provided with an engine, as well as a transmission having a motor/generator, a stationary member, and a planetary gear set. The engine and the motor/generator are separately selectively connectable to one of the drive axle assemblies by engagement of different ones of the torque-transmitting mechanism to transfer torque to that drive axle assembly. One or both of the engine and the motor/generator is also selectively connectable to the other drive axle assembly by engagement of another one of the torque-transmitting mechanisms to transfer torque to the other of drive axle assembly.