We investigate the problem of reflection and refraction of thermoelastic waves at a magnetized solid-liquid interface in presence of initial stress. In the context of Green-Lindsay and coupled thermoelastic theories of thermoelasticity, the problem has been solved and the effect of magnetic field, external heat sources, and initial stress on p-, T-, and SV-waves propagation have been discussed. The boundary conditions at the interface for displacement continuity, vanishing the tangential displacement, continuity of normal force, tangential force, and continuity of temperature are applied. The amplitudes ratios for the incident p-, T-, and SV-waves have been obtained. The effect of the initial stress, heat sources, and magnetic field on the reflection and transmitted coefficients for the incident waves have been discussed.