A hybrid transmission is provided with a motor and a torque-transfer device is operable to transfer torque from the motor to a transmission input member upstream in power flow from the transmission gearing arrangement. The torque transfer device may be a fluid coupling, such as a torque converter, including a torque converter lock-up clutch. In other embodiments, the torque transfer device is a launch clutch that may be either a wet clutch engagable via pressurized transmission fluid, or a dry clutch, such as used in a manual transmission. A disconnect clutch is selectively engagable to operatively connect an engine connection member with the motor to permit the motor to start the engine, such as after a stop. Many embodiments of the transmission include a one-way clutch arranged in parallel with the disconnect clutch. A method of starting the engine using such a transmission is also provided.