Magnetoelectric coupling terms are derived in piezoelectric/magnetostrictive (multiferroic) thin film heterostructures using Landau-Ginzburg free energy expansions in terms of three order parameters: strain, magnetization, and electric polarization. Strain is eliminated using a particular set of interface boundary conditions. Then, a general effective medium method is used to calculate the ferromagnetic resonance frequency in a BaTiO3/NiFe2O4 superlattice. This method differs from existing methods for treating magnetoelectric heterostructures since the magnetic and electric dipolar fields are not assumed constant but vary from one film to another. The ferromagnetic resonance frequency shift is calculated as a function of applied electric field and is compared to some experimental results.