An X-ray reflectivity set-up to study buried interfaces at beamline BL9 of the electron storage ring DELTA is presented. The structure of solid-gas and solid-liquid interfaces can be investigated using X-rays with incident energies of about 27 keV. A detailed description of the set-up is given and its performance is demonstrated by a discussion of selected applications, i.e. protein adsorption at the solid-liquid interface and gas adsorption at the solid-gas interface at elevated pressures.