A hybrid transmission is provided that is configured to shift between the hybrid series operating mode and the compound-split operating mode synchronously, without slipping any torque-transmitting mechanisms. The transmission includes an input member operatively connected with the engine, an output member, and a plurality of selectively engageable torque-transmitting mechanisms. A gearing arrangement and first and second motor/generators operatively connected with the gearing arrangement are also provided. A first of the torque-transmitting mechanisms is engaged to establish a hybrid series operating mode between the input member and the output member, and a second of the torque-transmitting mechanisms is engaged to establish a compound-split operating mode between the input member and the output member. The shift between the hybrid series operating mode and the compound-split operating mode is synchronous without slipping the torque-transmitting mechanisms and occurs while the engine is on.