A radiative diffusion problem which gives rise to a wave front with two-dimensional structure is considered. Particular emphasis is placed on the description of the wave front resulting from a point source of energy liberated instantaneously at the interface between two homogeneous half-spaces. By a combination of similarity and moments methods the problem is reduced to a second-order nonlinear ordinary differential equation describing the position of the wave front. This equation is solved analytically in the almost spherical and highly nonspherical limits. Numerical results for the partition of energy between the two half-spaces are given.