Epitaxial ZnSe/CdTe/ZnSe heterostructures were successfully fabricated by molecular beam epitaxy on GaAs(001) wafers despite the large in-plane lattice mismatch (14.3%) between the two II-VI materials. X-ray reciprocal space maps and selected area diffraction results indicate single-phase, (111)-oriented growth of CdTe onto the lower ZnSe(001) cladding layer, and single-phase, (111)-oriented growth of the topmost ZnSe layer, with a small inhomogeneous residual strain within the CdTe layer. Cross-sectional transmission electron micrographs reveal a distribution of rotational microtwins within the (111)-oriented layers near each interface. The low-temperature near-band-edge photoluminescence from the CdTe layer is free-exciton related, and exhibits a linewidth of only 5-6 meV.