A full wave integral equation method for dielectrics and conductors is developed based on the augmented electric field integral equation. This method rigorously models dielectrics and conductors to solve circuit interconnects and packaging problems. By treating the two regions rigorously and solving both the internal and external problems with the augmented electric field integral equation, accurate results for dielectrics are obtained efficiently. The conductors, however, are modeled as highly lossy dielectrics. A novel integration technique is analyzed and adopted to capture the wave properties inside the conductors. A strategy of integrating this method with the mixed-form fast multipole algorithm is presented. With the fast algorithm, more complicated, multi-scale structures with a large number of unknowns can be solved. Some numerical results show the capability of this method to solve realistic circuit problems efficiently and accurately.