This paper presents a study of magnetoelectric (ME) properties of the PZT/Terfenol-D composite with a varying number of layers. The composite consists of piezoelectric and magnetostrictive phases that are mechanically coupled. The purpose of this setup is to gain control over the electric polarization of a material via an external magnetic field. Unlike most similar composites, our samples utilize a commercial piezoelectric patch instead of pure PZT. At present, researchers face two main problems regarding magnetoelectric materials: (i) the effect is observed far below room temperature for single-phase materials, and (ii) the ME coupling is too weak to be commercially viable. Our research was carried out via the lock-in technique on two PZT/Terfenol-D samples we synthesized. Relatively strong room-temperature magnetoelectric coupling between piezoelectric and magnetostrictive phases was observed for both samples. Two types of characteristics were investigated: (i) ME voltage versus magnetic AC field frequency, and (ii) ME voltage versus magnetic DC field. We detected multiple, grouped signal peaks ascribed to different resonance modes. Uniquely, the peaks form band-like characteristics which might be an important step in bringing the materials closer to wider commercial use.