We present a general algorithm for calculating the spatial variation of the shear viscosity and thermal conductivity through an equilibrium solid-liquid interface using the zero-flux version of the boundary fluctuation theory. In the case of an equilibrium interface between a high melting point Lennard-Jones solid and a low melting point Lennard-Jones liquid, we find that the transport coefficients deviate from the bulk values only in a narrow layer close to the interface. We observe a sliding friction of the liquid against the surface of the solid that increases with increased wetting of the solid by the liquid. The thermal conductivity, in contrast, is suppressed in the interfacial region, irrespective of how the liquid wets the solid.