The model of the generalized linear micropolar magneto-thermoviscoelastic theory is presented in this paper. It can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. If some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. The magneto-thermo- viscoelastic waves at an interface between two micropolar viscoelastic solid mediums are discussed with the model. Using continuous conditions, the general frequency equations are obtained. Also as a validation, if one media is replaced by vacuum, we have deduced the frequency equation of Rayleigh wave. And if the problem is reduced to elastic case, it coincides with the results of Ewing et al.