High-quality radio occultation data were acquired as the Voyager 2 spacecraft flew behind Jupiter on July 10, 1979. We have conducted a thorough analysis of dual-frequency data from the ionosphere using a new method of data processing based on scalar diffraction theory. The method is capable of deciphering the effects of multipath propagation, which had not previously been possible for these data. This allows retrieved vertical profiles of electron number density to be extended downward throughout the lower ionosphere. The electron density profile at occultation entry (66 ¿S, 258 ¿W) has a topside scale height of 1020 km, consistent with previous results. New results include a peak density of 3.5¿105 cm-3 at a height of 640 km above the 1-bar pressure level. In addition, the lower side of the main peak contains quasi-sinusoidal density oscillations with a vertical spacing of 25--40 km at altitudes of 450--600 km. These appear to signal the presence of upward propagating gravity waves. The electron density profile at occultation exit (51 ¿S, 148 ¿W) exhibits a peak density of 2.3¿105 cm-3 at an altitude of 1900 km, and the topside has a uniform scale height of 850 km. These characteristics of the upper ionosphere, where the principal ion is believed to be H+, are consistent with earlier results. New results include two secondary peaks at lower altitudes. An intermediate layer, where the principal ion may be H3+, is centered near 1000 km with a peak density of 4.6¿104 cm-3. A lower layer, possibly composed of metallic ions, is situated between 200 and 550 km with densities of 2--12¿104 cm-3. The latter contains multiple, thin layers of ionization at altitudes of 300--450 km, which may be the result of vertical shear in the zonal wind or plasma instabilities. The height-integrated Pedersen conductivity is about 0.5 and 0.4 mho at entry and exit, respectively. ¿ 1998 American Geophysical Union