The nature of mechanical strain-mediated converse magnetoelectric effect (CME) has been studied in multiferroic composites of single-crystal like thin films of nickel ferrite (NFO) and polycrystalline lead zirconate titanate (PZT). Ferrite films of thickness 0.45 to 1 micron were prepared by Pulsed Laser Deposition on lattice-matched (100) and (110) substrates of magnesium gallate (MGO) and cobalt gallate (CGO) that resulted in elimination of antiphase boundaries and magnetic parameters comparable to bulk single crystals. Ferromagnetic resonance under a static electric field E was utilized for studies of CME effects in composites of PZT and NFO films on the substrates. The in-plane static magnetic field H was applied along the principal crystallographic axes of the ferrite film to study its influence on CME.The E-induced ME anisotropy field HME was estimated from FMR data based on shift in resonance frequency with E in order to determine the ME constant A = HME/E. In composites with NFO films on (110) substrates (i) the ME coupling was stronger for films on CGO possibly due to a better lattice match and weaker substrate clamping than for films on MGO, (ii) A-values were the highest for H // [1,-1,0], and (iii) a negative A-value was inferred for H //[001]. For composites with NFO on (100) substrates the strongest ME coupling was measured for H along [001]. A first model for CME that takes into consideration both compressive and bending deformation in the composites is developed and results of the theory are in agreement with both the sign and magnitude of the measured ME coefficient A.The results of the studies presented here indicate the potential for use of the composites in self-biased E-tunable microwave devices.