Electric (e-) powertrain Noise, Vibration and Harshness (NVH) shows tonal behaviour due to the electromagnetic (EM) forces in the e-motor (leading to whistling noise) and the gear meshing (leading to whining noise). Tonal excitations activate different system modes as the motor speed changes, amplifying whistling and whining. Accurate prediction of resonance speeds and aggressive NVH is essential. Due to EM interactions, the e-motor exhibits EM torsional stiffness, affecting the system dynamics. Past studies considered EM stiffness in torsional vibration lumped parameter models, mostly neglecting flexible components (i.e. powertrain housing). In this work, the EM stiffness is calculated using the Frequency Response Function method and is included for the first time in the modal analysis of a three-dimensional e-powertrain model. This enables e-powertrain electromechanical coupling analysis during the design phase, considering the housing three-dimensional flexibility, a key NVH contributor. Conducting modal analysis with the EM stiffness shows effects on the system natural frequencies, along with the mode shapes at different frequency ranges and operating speeds, establishing an accurate design method to describe the e-powertrain dynamics and provide clearer insight on the NVH physics.