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The work is devoted to the theoretical investigation of the quasi-static magnetoelectric interaction in three-layer structures consisting of a piezoelectric and two magnetic layers with positive and negative magnetostriction. Using the system of elasto- and electrostatics equations for the piezoelectric and magnetostrictive phases, expressions for the electrical response of the structure in a magnetic field are obtained. The contributions from longitudinal and bending deformations are taken into account in value of ME interactions. It is shown that the use of an asymmetric three-layer asymmetric structure leads to an increase in the magnitude of the ME interaction by almost an order of magnitude compared to a two-layer structure. The dependences of the effect magnitude on the thickness of the third layer for the nickel/lead zirconate titanate/metglas structure are presented. Keywords: piezomagnetostrictive composites, magnetostriction, piezoelectricity, magnetoelectric effect, gyrator, harvester.