A powertrain is provided that includes an engine as well as a transmission having an input member and an output member. The powertrain also includes a motor/generator that has an energizable stator, a first rotor and a second rotor (i.e., a dual rotor motor). Both of the rotors are rotatable via energization of the stator. A first torque-transmitting mechanism, referred to as the engine clutch, is selectively engagable to connect the engine for common rotation with one of the first and the second rotors. A second torque-transmitting mechanism, referred to as the motor clutch, is selectively engagable to connect the first rotor for common rotation with the second rotor. The transmission input member is continuously connected for common rotation with the other of the first and second rotors.