Magnetoelectric composites of the ferrite phase Cu${}_{1−x}$Co$_x$Fe$_2$O$_4$ (where x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) and the ferroelectric phase PbZr$_{0.58}$Ti$_{0.42}$O$_3$ were synthesised by conventional solid-state reaction method. X-ray diffraction studies reveal the coexistence of the ferrite phase with cubic spinel structure and ferroelectric phase with perovskite structure. Ferrite/PZT/ferrite, PZT/ferrite/PZT trilayered structures are fabricated using screen printing technique. The variation of dielectric constant and loss tangent in the frequency range 100 Hz to 5 MHz and with temperature at a fixed frequency of 1 kHz were studied. Dielectric properties are explained based on dielectric relaxation. At room temperature, AC resistivity decreases with increase in frequency which is due tothe hopping frequency of charge carriers at equivalent ionic sites. Conductivity measurements confirm the small polaron hopping mechanism. Transverse ME voltage coefficient (α$_{E31}$) increases gradually attaining the maximum value at 400 Oe and then decreases beyond that with respect to the applied DC bias magnetic field. The variation of α$_{E31}$ with applied DC external bias magnetic field was explained based on the domain growth and reorientation of domains with the applied magnetic field.