Magnetoelectric (ME) coupling in the composites is mediated by the mechanical stress and one would expect orders of magnitude stronger coupling when the frequency of the ac field is tuned to acoustic mode frequencies in the sample than at non-resonance frequencies. A model is presented for the increase in ME coupling in magnetostrictive-piezoelectric bilayers for the longitudinal, radial, and bending modes in the electromechanical resonance region. We solved the equation of medium motion taking into account the magnetostatic and elastostatic equations, constitutive equations, Hooke's law, and boundary conditions. We estimated the ME voltage coefficient for direct ME effect and ME susceptibility for inverse ME coupling. The frequency dependence of the ME voltage coefficient and ME susceptibility reveals a resonance character in the electromechanical resonance region. Then we considered ME interaction in the magnetoacoustic resonance region at the coincidence of electromechanical and magnetic resonance. Variation in the piezomagnetic coefficient with static magnetic field for magnetic layer results in a dependence of ME voltage on applied bias magnetic field. As an example, we considered specific cases of cobalt ferrite or yttrium-ferrum garnet - lead zirconate titanate and nickel/permendur - lead zirconate titanate bilayers. Estimated values of ME voltage coefficient versus frequency profiles are in agreement with data.