This paper presents an exact solution to the equations of radiative transfer for a generalization of the Uniform-Picket-Fence model discussed in a previous work. Here the absorption coefficient is allowed to take N different values over the frequency spectrum. Case's method is used to construct the normal mode solutions to the set of N coupled integral equations. Then half-range completeness and orthogonality theorems are proved that enable one to solve typical half-space problems. Explicitly, the asymptotic solution to the Milne problem is developed, including the extrapolated end point, while implicitly the complete solution is available.