This paper deals with the study of magnetoelectric structures which could allow the emergence of a new class of microwave tunable devices. Our interest was focused on composite magnetoelectric structures which associate piezoelectric substrates and magnetostrictive layers in order to get a variation of microwave permeability thanks to an electric field. Poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] copolymers and lead magnesium niobate-lead titanate (PMN-PT) single crystals were used to introduce strains in ferromagnetic layers. Thus, FeCoB/P(VDF-TrFE) and FeCoB/PMN-PT multilayers were investigated through static and dynamic measurements. We demonstrated a strong magnetoelectric effect in a FeCoB/PMN-PT bilayer. Indeed, the FeCoB film permeability decreases from 800 to 1 under 125 V in the 0.5-1.3 GHz frequency band.