Polycrystalline bilayer thin film of multiferroic [Ba(Zr0.2Ti0.8)O-3-0.5(Ba0.7Ca0.3)TiO3]/CoFe2O4([BZT-0.5BCT]/CFO) has been deposited on Pt/Si (100) substrate using a pulsed laser deposition technique. The dielectric analysis reveals a significant change in the dielectric constant (similar to 39% at a typical frequency of 100 Hz) at room temperature when a magnetic field is applied, in addition to a substantial improvement in the saturation polarization. A low leakage current density (similar to 5 x 10(-7) A/cm(2)) and a high magnetoelectric coupling coefficient (alpha(E)) both in the transverse (similar to 2.085 V/Oe cm) as well as in the longitudinal (similar to 0.708 V/cm Oe) directions, indicate in-principle usability of this system for multifunctional device applications in thin film form.