•Mixing of electric and magnetic field frequencies was observed in a heterostructure.•Nonlinearity of converse ME effect arises due to nonlinearity of magnetoelasticity.•A theory describing converse ME effects in composite structures has been developed. Nonlinear magnetoelectric effects in a disk-like heterostructure composed of a layer of amorphous ferromagnet (FeBSiC) mechanically coupled to a layer of piezoelectric ceramics (lead zirconate titanate) were studied both experimentally and theoretically. The structure was excited by alternating electrical and magnetic fields far from its acoustic resonance frequency. This induced changes in the magnetic induction within the heterostructure which were recorded using an electromagnetic coil. The experiments were performed for excitations with electric and magnetic fields up to 250 V/cm and 6 Oe, respectively, and bias permanent magnetic fields up to 60 Oe. For large excitation fields, a generation of the second harmonic and harmonics corresponding to the sum and difference frequencies were observed. The coefficient of the frequency doubling for the converse magnetoelectric effect and the coefficient of mixing of electrical and magnetic field frequencies were found to be 4.6∙10−6 G cm2/V2 and ∼1∙10−2 G cm/(Oe∙V), respectively. A simple theoretical model qualitatively describing the experimental findings was proposed. It was shown that the nonlinearity in the converse magnetoelectric effect arises due to the nonlinear dependence of magnetic induction in the ferromagnetic layer on mechanical stress.