This paper proposes a mathematical model for 3D nonlinear magnetoelectric effects in heterogeneous composite structures. Through the coupling of the Finite Element Method (FEM) with the Boundary Element Method (BEM), only the active material is explicitly considered, and thus a single mesh is used to support all phenomena. A mixed formulation is used to model the magnetic phenomena, a vector potential formulation in the volume and a scalar potential formulation in the free space domain. Material laws for the magnetostrictive composite phase are derived from partial derivatives of a scalar invariant’s formulation of the Helmholtz free energy. The coupled problem is solved by iteratively solving single-physics problems, and the full algorithm is applied to the modeling of a test case.