<p>Polymer-based magnetoelectric materials, a type of three-phase polymer matrix smart composites, have emerged as a promising solution for enabling smart structural systems with advanced functionalities and demonstrating great potential for practical engineering applications. These smart composites come into contact with different rigid engineering components with the time-dependent multiphysics response. This study reports a novel hybrid element model for addressing the three-dimensional frictional sliding contact problem between a rigid spherical punch and such materials, in which the electro-magneto-viscoelastic behavior induced by the polymer matrix, piezoelectric phases, magnetostrictive phases are taken into account. Frequency response functions for unit electric, magnetic, and mechanical loads are derived based on the elastic–viscoelastic correspondence principle. During the transient regime analysis, the contact pressure, in-plane stress, and electric/magnetic potentials are numerically computed using the conjugate gradient method and discrete convolution-fast Fourier transform. The study delves into the combined effect of the surface electric/magnetic charge density and friction coefficient on the time-dependent contact behavior.</p>