In this paper, we discuss a theoretical model with experimental verification for the resonance enhancement of magnetoelectric (ME) interactions at frequencies corresponding to bending-tension oscillations. A dynamic theory of arbitrary laminated magneto-elasto-electric bars was constructed. The model included bending and longitudinal vibration effects for predicting ME coefficients in laminate bar composite structures consisting of magnetostrictive, piezoelectric, and pure elastic layers. The thickness dependence of stress, strain, and magnetic and electric fields within a sample are taken into account, as such the bending deformations should be considered in an applied magnetic or electric field. The frequency dependence of the ME voltage coefficients has obtained by solving electrostatic, magnetostatic, and elastodynamic equations. We consider boundary conditions corresponding to free vibrations at both ends. As a demonstration, our theory for multilayer ME composites was then applied to ferromagnetic-ferroelectric bilayers, specifically Metglas-PZT ones. A theoretical model is presented for static (low-frequency) ME effects in such bilayers. We also performed experiments for these Metglas-PZT bilayers and analyzed the influence of Metglas geometry (length and thickness) and Metglas/PZT volume fraction on the ME coefficient. The frequency dependence of the ME coefficient is also presented for different geometries (length, thickness) of Metglas. The theory shows good agreement with experimental data, even near the resonance frequency.