The reflection and refraction of thermoelastic waves at an interface of two semi-infinite media in contact with two relaxation times are studied following Green and Lindsay's theory. The analytical expressions for the partition of energy are carried out. The results for various values of the angle of incidence for the partition of energy are presented in the context of two different cases: (i) liquid-liquid and (ii) liquid-solid. The numerical results are represented graphically to aid the comparison with Lord and Shulman's theory in order to see the effect of the second relaxation time.