The method of singular eigenfunction expansions is applied to the time-independent one-speed Milne problem in which there are two half-space media. It is assumed that scattering in each medium is at most linear in the cosine of the scattering angle; closed form expressions are then obtained for the expansion coefficients. Numerical results show the dependence upon the scattering parameters of the extrapolation distance and the discontinuities in the asymptotic densities and currents at the interface. These results give the proper boundary conditions to be applied when using diffusion theory in problems involving two or more plane layers which are thick as compared to the mean-free-paths of the media.