The optical path transformation is applied to reduce the one-speed neutron transport equation for a class of composite subcritical slabs to single-region problems. The class idealises, within the uncertainty of the one-speed model, a variety of practical situations such as U-D₂O-C-Zr-Pb or Pu-U-Na-Fe symmetric reactor assemblies; which may possibly contain a symmetrically anisotropic neutron source. A closed form double series solution, which turns out to be quite convenient for design and optimisation purposes, has been obtained, in terms of discontinuous functions for the multi-regional angular flux by application of a double finite Legendre transform. The double transform blends the conventional P_N method with the spatial polynomial expansion method. Disadvantage factor evaluations for a U-C lattice cell resulting from a low-order P₀P₁ approximation of this method are found to be in full agreement with hybrid diffusion-transport estimates.