We study theoretically the effects of exciton bound states on the reflectivity of semiconductor superlattices and thin films. We consider direct gap semiconductors and assume extrinsic potentials near surfaces to model the exciton interactions. Using a multistep method and the transfer matrix approach, we solve analytically the polariton exciton equations for s-polarized light. Results are presented for the excitonic transition of CdS and interpreted in terms of exciton bound states and Fabry-Pérot resonances of the transverse modes. We find that for the superlattice the reflectivity peaks of the high-energy bound states are notably enhanced as compared with the corresponding ones of the single isolated film.