The magnetoelectric (ME) characterization of bilayers of lead zirconate titanate (PZT) and single crystal or hot-pressed polycrystalline lanthanum strontium manganite (LSMO) are discussed. Data on ME voltage coefficient have been obtained as a function of strength and orientation of bias magnetic field H, temperature, and frequency. The bilayers exhibit superior ME coupling compared to thick film multilayer composites and the strongest ME interactions are measured for samples with single crystal LSMO. Bilayers with single crystal LSMO show strong dependence of ME coefficient on H orientation and temperature, with a maximum value of 190 mV/cm Oe at 86 K. The frequency dependence of ME coefficient reveals a resonance enhancement due to radial acoustic modes. There is excellent agreement between theory and data for the H variation of ME coefficients.