Motivated by applications to electrophoretic techniques for bioseparations, we consider transient one-dimensional convection-diffusion through a medium in which the solute diffusivity and convective velocity undergo step changes at a prescribed position. An exact method of solution of the governing transport equations is formulated in terms of a largely analytical approach representing a novel alternative to the self-adjoint formalism advanced by Ramkrishna and Amundson (1974, Chem. Engng Sci. 29, 1457-1464), and applied recently by Locke and Arce (1993, Chem. Engng Sci. 48, 1675-1686) and Locke et al. (1993, Chem Engng Sci. 48, 4007-4022). A concentration boundary layer of O(Pe(-1)) thickness is found to form at the upstream side of the interface. No concentration boundary layer exists on the downstream side. The exact solution is supplemented with an asymptotic analysis for large Peclet numbers, Pe. Detailed study of the boundary layer reveals interesting features of the local dynamical processes whereby the interface-infinitesimally thin macroscopically-appears as an effective source or sink of the solute content. The asymptotic analysis has direct utility in accurate prediction of concentration profiles for high Peclet number operations where analytical approaches break down and finite-difference methods require tremendous computational time to achieve sufficient accuracy and resolution.