The present paper is concerned with the propagation of Stoneley waves at the interface of two couple stress thermoelastic medium in context with Lord and Shulman (LS) and Green and Lindsay (GL) theories of thermoelasticity. It is observed that shear wave get decoupled from rest of the motion. After developing the formal solution, the secular equation for surface wave propagation is derived. The dispersion curve giving the phase velocity and attenuation coefficient related to wave number are plotted graphically to depict the effect of thermal relaxation times. The amplitude ratios of displacement components and temperature distribution are also computed numerically and shown graphically to depict the effect of thermal relaxation times. Some special cases are also deduced from the present investigation.