We propose and characterize oil-in-gelatin dispersions that approximate the dispersive dielectric properties of a variety of human soft tissues over the microwave frequency range from 500 MHz to 20 GHz. Different tissues are mimicked by selection of an appropriate concentration of oil. The materials possess long-term stability and can be employed in heterogeneous configurations without change in geometry or dielectric properties due to osmotic effects. Thus, these materials can be used to construct heterogeneous phantoms, including anthropomorphic types, for narrowband and ultrawideband microwave technologies, such as breast cancer detection and imaging systems.