A new approach to optical remote sensing of the Earth's atmosphere using a combination of extinctive and refractive stellar occultation measurements is presented. In this combined method, spectrographic imagers are used to measure the wavelength-dependent atmospheric extinction of starlight while a co-aligned imager is used to measure the atmospheric refraction along the same line of sight. By simultaneously measuring both the refraction and extinction of the starlight, the composition-dependent extinction measurements can more accurately probe the Earth's lower atmosphere, where refraction effects are significant. The refraction measurements provide the bulk atmospheric properties and the actual light path through the atmosphere, both of which are necessary to correctly infer the total extinction in the refractive regime. The technique is demonstrated on a proof-of-concept basis using data from the Ultraviolet and Visible Imagers and Spectrographic Imagers (UVISI) on the Midcourse Space Experiment (MSX) satellite. These preliminary results show that the combined approach has the potential to be a powerful, self-calibrating method for remotely sensing the Earth's atmosphere in general and for the determination of ozone profiles in the stratosphere and upper troposphere in particular.