The multilayers of ferroelectric (FE) Pb(Zr, Ti)O3 (PZT) and ferromagnetic (FM) CoFe2O4 (CFO) thin films with 3, 5, and 9 layers having configurations PZT/CFO (PC) and CFO/PZT (CP) were fabricated by pulsed laser deposition technique. We have investigated the effect of inter-diffusion at the interface of multilayers (MLs) and reversing the order of FE and FM layers in the multilayers configuration on the electrical/magnetic properties. The TEM of the films showed that the layer structure was not maintained and the inter-diffusion of the CFO into PZT and vice verse were observed at the interface of MLs. Both the PC and CP configurations of multilayer films exhibited pseudo FE hysteresis loop and proper FM hysteresis loops at room temperature. Reversing the multilayer configuration from CP to PC resulted in increasing the pseudo remanent polarization, however this behavior was not observed in magnetic properties. The frequency and temperature dependences of the impedance and modulus spectroscopy of the multilayer PC and CP films were studied in the ranges of 102 to 106 Hz and 200 to 650 K respectively. The electrical response of all multilayer films investigated could be resolved into two contributions. We attributed these to the grain and grain boundary effects in impedance and modulus formalism. We found that the difference between the grain and grain boundary capacitive effect decreased due to increase of the number of layers.