An effective medium theory is formulated which reproduces many of the observed electrical and elastic characteristics of sedimentary rocks within a unified framework. The effective medium consists of fluid, solid, and cement components, with the component material properties related to those of the composite through a differential effective medium (DEM) scheme. The resulting microstructure of the composite both conducts electricity through the fluid phase and supports shear. Besides deriving Archie's law, the theory gives an excellent account of the shear-wave and compressional-wave velocity correlations, and predicts corrections to the Wyllie equation that are consistent with observed deviations. The three-component DEM also accommodates clay conductivity and finite-frequency dielectric behavior.