In the present work, we study the hysteretic behavior in the electric-field-dependent capacitance and the current characteristics of 0.5Ba(ZrTi)O-0.5(BaCa)TiO (BCZT)/ZnO bilayers deposited on 0.7 wt % Nb-doped (001)-SrTiO (Nb:STO) substrates in a metal-ferroelectric-semiconductor (MFS) configuration. The X-ray diffraction measurements show that the BCZT and ZnO layers are highly oriented along the c-axis and have a single perovskite and wurtzite phases, respectively, whereas high-resolution transmission electron microscopy revealed very sharp Nb:STO/BCZT/ZnO interfaces. The capacitance-electric field ( C- E) characteristics of the bilayers exhibit a memory window of 47 kV/cm and a capacitance decrease of 22%, at a negative bias. The later result is explained by the formation of a depletion region in the ZnO layer. Moreover, an unusual resistive switching (RS) behavior is observed in the BCZT films, where the RS ratio can be 500 times enhanced in the BCZT/ZnO bilayers. The RS enhancement can be understood by the barrier potential profile modulation at the depletion region, in the BCZT/ZnO junction, via ferroelectric polarization switching of the BCZT layer. This work builds a bridge between the hysteretic behavior observed either in the C- E and current-electric field characteristics on a MFS structure.