Three neutron transport problems involving two different media are solved in two-group theory for isotropic scattering based on the singular-eigenfunction-expansion solution of the transport equation. This work has two purposes: First, it is shown that two-media problems in two-group theory can be reduced to regular computational forms using the half-range orthogonality theorem; second, in support of benchmark activities, three model problems are defined, and their solutions are reported based on an exact theory.