Multilayered magnetoelectric materials are of great interest for investigations due to their unique tuneable properties and giant values of magnetoelectric effect. The flexible layered structures consisting of soft components can reveal lower values of the resonant frequency for the dynamic magnetoelectric effect appearing in bending deformation mode. The double-layered structure based on the piezoelectric polymer polyvinylidene fluoride and a magnetoactive elastomer (MAE) with carbonyl iron particles in a cantilever configuration was investigated in this work. The gradient AC magnetic field was applied to the structure, causing the bending of the sample due to the attraction acting on the magnetic component. The resonant enhancement of the magnetoelectric effect was observed. The main resonant frequency for the samples depended on the MAE properties, namely, their thickness and concentration of iron particles, and was 156–163 Hz for a 0.3 mm MAE layer and 50–72 Hz for a 3 mm MAE layer; the resonant frequency depended on bias DC magnetic field as well. The results obtained can extend the application area of these devices for energy harvesting.