The present problem deals with the study of propagation of Stoneley waves at the interface of two dissimilar isotropic modified couple stress thermoelastic with mass diffusion medium in the context of Lord-Shulman (L-S), Green-Lindsay (G-L) theories of thermoelasticity. The dispersion equation of Stoneley waves is derived in the form of determinant by using appropriate boundary conditions. The dispersion curves giving the values of determinant of secular equation, Stoneley waves velocity and attenuation coefficient with respect to angular velocity for different values of wave number in the absence and presence of mass diffusion are computed numerically and shown graphically.