By using the CHAllenge Minisatellite Payload (CHAMP) radio occultation (RO) data, a description of different types of the ionospheric impacts on the RO signals at the altitudes 30-90 km of the RO ray perigee is given and compared with the results of measurements obtained earlier in the satellite-to-Earth communication link at frequency 1.5415 GHz. An analytical model is introduced for describing propagation of radio waves in a stratified medium consisting of sectors with spherically symmetric refractivity distribution. This model gives analytical expressions for the phase, bending angle, and refractive attenuation of radio waves and is applied to the analysis of radio wave propagation phenomena along an extended path including the atmosphere and two parts of the ionosphere. The model explains significant amplitude and phase variations at altitudes 30-90 km of the RO ray perigee and attributes them to inclined ionospheric layers. Based on this analytical model, an innovative technique is introduced to locate layers in the atmosphere and ionosphere. A necessary and sufficient criterion is obtained for a layer to be located at the RO ray perigee. This criterion gives both qualitative and quantitative estimation of the displacement of an ionospheric and/or atmospheric layer from the RO ray perigee. This is important, in particular, for determining the location of wind shears and directions of the internal wave propagation in the lower ionosphere, and, possibly, in the atmosphere.