The incorporation of room temperature ionic liquids (ILs) into dielectric elastomer composites is currently generating great interest due to their potential applications in soft actuators and optical-related devices. Experiments have shown that the electrical properties of IL enhanced soft composites (ILESCs) are dependent on AC (alternating current) frequency of the electrical loading. This current work helps develop a mixed micromechanical model with the incorporation of an electric double layer (EDL) to predict the electrical properties of the ILESCs while revealing the physical mechanisms (including crowding and overscreening structures, percolation thresholds, interfacial tunneling, Maxwell-Wagner-Sillars polarization) that underpin the phenomena. Particularly, Bazant-Storey-Kornyshev (BSK) phenomenological theory is integrated into the EDL surface diffusion model for the first time to evaluate the influence of crowding and overscreening effects. The results show excellent agreement with experimental data of IL enhanced PDMS composites over the frequency range from 1 Hz to 10 GHz. Parametric analysis from the perspective of designing is conducted to explore the methods for optimization of ILESCs with high dielectric constants and frequency-dependent stability. It is found that an IL with a smaller size and aspect ratio increases the dielectric constant of the ILESCs more significantly below the interface relaxation frequency. Increasing the surface charge density of the matrix and using ILs delay the frequency-facilitated dielectric response, which is beneficial to maintain the dielectric stability of the ILESCs.