Reflection and refraction of harmonic SH-waves from the interface of two dissimilar media with microheterogeneity is studied. The effect of the microheterogeneity on the overall behavior of the media is taken into account by adding higher order displacement gradients in the stress-strain relationship. It is found that a harmonic wave reflects back with the same angle of the incident wave, like in a classical case. However, it is found that the direction of propagation of the refracted wave is dependent on the wave number. It is also shown that the critical angle for which the incident wave cannot be transmitted to the other half plane is dependent on the wave number.