Hydraulic pressing and screen printing methods are used to create particulate magnetoelectric composites and laminated trilayered thick‐film composites. X‐ray diffraction studies reveal the presence of cubic spinel and tetragonal perovskite structures for individual powders of ferrite CuFe2O4 and ferroelectric‐phase PbZr0.58Ti0.42O3. The dielectric constant of particulate composites decreases with increasing frequency around 1 MHz and beyond that frequency, a saturation state is attained. However, for laminated films, the dielectric constant decreases up to 1 MHz and then increases. The maximum dielectric constant at low frequency for particulate CuFe2O4/PZT composites is around 72.2, whereas for laminated CuFe2O4/PZT/CuFe2O4 composites it is 4.97 and for PZT/CuFe2O4/PZT composites is 5.24. Loss tangent exhibits the same trend as dielectric constant with frequency, which is explained by space charge polarization and is consistent with Koop's phenomenological theory. The dielectric constant's variation with temperature describes the contribution of electric dipoles to polarization and both composites exhibit absorption peaks. The semiconducting nature of both particulate and laminated composites can be seen in the DC resistivity graph with frequency and as frequency increases, DC resistivity decreases for both composites, which is explained by the small polaron‐hopping phenomenon. The magnetoelectric coupling effect for particulate composites (44 mV Oe−1cm−1) is also found to be small when compared to laminated trilayered composites (CuFe2O4/PZT/CuFe2O4—105 mV Oe−1cm−1 and PZT/CuFe2O4/PZT—68 mV Oe−1cm−1).