The magnetoimpedance effect and the converse magnetoelectric effect in a planar heterostructure consisting of mechanically bonded layers of amorphous ferromagnet FeBSiC and piezoelectric lead zirconate titanate are studied. Magnetoimpedance was observed in the frequency range of 0.1-40 MHz and bias dc magnetic field of 0-300 Oe; the maximum magnitude of the effect at a frequency of 10 MHz reached 12%. The converse magnetoelectric effect was observed in magnetic fields of 0-50 Oe; the maximum value of the effect at the structure acoustic resonance frequency of 40 kHz was 1.45 G/(V/cm). Amplitude modulation of the magnetoimpedance by an electric field at the resonance frequency of the structure with a coefficient of ~1∙10─2 is found. Modulation occurs as a result of a combination of the piezoelectricity and magnetostriction of the layers, which leads to a change in the transverse magnetic permeability and the thickness of the skin-layer of the ferromagnet.