•Direct and converse magnetoelectric effects observed in flexible FeBSiC-PVDF structure.•Converse ME effect arises due to elastomagnetic nonlinearity of ferromagnetic layer.•Field dependences of ME conversion efficiencies are well explained by the theory. The direct and converse magnetoelectric (ME) effects in a flexible structure containing a mechanically coupled layers of amorphous ferromagnet FeBSiC and a piezo-copolymer poly(viniledene fluoride trifluoroethylen) (P(VDF-TrFE)) are investigated. The mutual transformation of magnetic and electric fields in the structure arises due to a combination of magnetostriction and piezoelectric effects in the ferromagnetic and piezoelectric layer, respectively. The ME effects were induced by exciting the structure with alternating magnetic fields of 0–100 kHz frequency and 1–5 Oe amplitude, or alternating electric fields of amplitudes up to 500 V/cm in the presence of a constant H field. For the direct ME effect the conversion coefficient reached 7.2 V/(cm·Oe) at a bending resonance frequency of 412 Hz and 44 V/(cm·Oe) at a planar resonance frequency of 25.15 kHz. Increasing the excitation magnetic field at the bending resonance frequency, the nonlinear second harmonic generation with an efficiency of 0.24 V/(cm·Oe2) was observed. For the converse ME effect, the conversion coefficient at the planar resonance frequency was 0.09 G·cm/V. The dependences of the efficiencies for the direct and converse ME transformations on the constant field and the amplitudes of the excitation fields are well explained by theory. These results could be used to develop magnetic and electric field sensors, as well as autonomous energy harvesting sources.