The magnetoelectric (ME) effect in composites, a strain-mediated coupling phenomenon between piezoelectric and magnetostrictive phases, has a wide range of technological applications. Here, ME coupling phenomena are explored in Pb-free piezoelectric, 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 and piezomagnetic NiFe2O4 bilayer laminate composites. The direct and converse ME coupling strengths are found to be enhanced at the electromechanical resonance modes, rather than at the off-resonance frequencies. Here, it is proposed to further enhance the ME coupling strength at electromechanical resonance modes by the in-phase superimposition of the radial and second bending modes via varying the bilayer thickness, which, in turn, varies the volume fraction of the bilayer. The proposed enhanced ME coupling is experimentally demonstrated at a theoretically envisaged bilayer thickness of about 1.8 mm. This results in a large direct ME coupling coefficient of 22.5Vcm-1Oe-1, which is around 100% more than the values observed at individual resonance modes. The results are further validated by calculations from theoretical models. The method adopted in this work gives a roadmap to the significant enhancement of the ME effect in laminate composites. © 2020 American Physical Society.