A transmission assembly for mounting to an external power-source includes an input shaft configured to receive power-source torque. The transmission assembly also includes an output member configured to transmit a transmission output torque to drive a load. The transmission assembly additionally includes a countershaft driven by and arranged parallel to the input shaft. The countershaft has a first gear-set rotatably mounted thereon and is configured to drive the output member. The transmission assembly also includes a second gear-set in mesh with the first gear-set and operatively connected to the output member. Furthermore, the transmission assembly includes an electric motor configured to be selectively connected to the input shaft via a first torque transfer device and to the output member via a second torque transfer device to thereby provide a variable electric motor internal torque input to the transmission assembly. A vehicle having such a transmission and power-source is also disclosed.