A singular perturbation technique is applied to the one-speed, one- dimensional neutron transport equation with isotropic scattering. Our technique extends previous singular perturbation applications to higher-order and reduces the transport problem to a series of diffusion theory problems in the interior medium and a series of analytically solvable transport problems in the boundary layers. Asymptotic matching links the two solutions, yielding boundary conditions and a composite expansion valid throughout the media. Our formulation generates an accurate correction for the material interface condition used in global diffusion theory calculations.