We study the propagation of shear horizontal waves between the interface of piezoelectric and piezomagnetic half-spaces with a magneto-electro-mechanical imperfect contact. Mechanical, electrical and magnetical imperfections are modelled by means of a spring, a capacitor and a inductor, respectively. A general expression for the dispersion relation not reported previously in literature is given in an explicit form, with the diverse limit cases analysed in detail. In some of these limit cases, new expressions are also obtained which predict the existence of interfacial waves. In the other cases, when already reported results exist, a comparison with them is done. Some physical interpretations are derived from the limit cases. The influence of mechanical, electrical and magnetical imperfect contacts are shown in some numerical examples.