The present paper deals with the propagating surfaces of weak discontinuities in semi-isotropic thermoelastic micropolar solids. Special attention is paid to the conditions of physical reliability of such processes. At this aim, the geometric and kinematic Hadamard–Thomas compatibility conditions of second order are used. Weak discontinuities of solutions of a coupled system of pseudovector partial differential equations of semi-isotropic micropolar thermoelasticity are studied. The velocities of the propagating wave surfaces of translational and spinor displacements are found. The classification of weak discontinuities of temperature increment, translational and spinor displacements, taking account of their spatial polarizations couples, is carried out. The relations between the amplitude factors of the weak discontinuity of the temperature field and the discontinuity vectors of translational and spinor displacements are obtained.