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The characteristics of both direct and converse magnetoelectric (ME) interactions in bilayer composite structures comprising layers of a commercially available magnetostrictive permendur CoFe alloy and different piezoelectric PZT ceramics are investigated in detail by the method of harmonic field modulation. It is shown that, given the optimum DC magnetic bias field, a high piezomagnetic coefficient in the alloy leads to increased efficiency of ME interactions. The resonant behavior of frequency dependencies of the magnetoelectric voltage is explained by excitation of bending and planar mechanical oscillations in the structures. The results are of interest for developing highly sensitive AC magnetic field sensors and magnetoelectric transducers for energy harvesting from mechanical vibrations.