Abstract A piezoelectric–piezomagnetic superlattice (PPS) is proposed to present the magneto-electric (ME) coupling wherein electric polarization induces magnetization or vice versa through the layer's coherent strain. We reveal that in PPS, the interaction of electromagnetic waves with the correspondent alternative piezoelectric and piezomagnetic superlattices through their vibrations excites the piezoelectric and the piezomagnetic phonon polaritons simultaneously. The polaritons couple with each other to give rise to a stop band, in which double negative permittivity and permeability can be realized, however negative refraction could not occur. The coupling also results in the huge dynamic ME effect which attributes to the large ME voltage coefficient in a BaTiO3–CoFe2O4 superlattice as large as 14.9 V cm−1 Oe−1.