A new full-wave surface impedance integral equation method is presented for three-dimensional arbitrary-shaped interconnect parasitic extraction in layered media. Various new ways of applying voltage and current excitations for electromagnetic-circuit simulation are introduced. A new algorithm is proposed for matrix formation of electromagnetic-circuit simulation, low frequency solution and layered media so that it can be easily integrated to a Rao-Wilton-Glisson based method of moment code. Two mixed potential integral equation forms of the electric field integral equation are adapted along with the Michalski-Mosig formulations for layered kernels to model electromagnetic interactions of interconnects in layered media over a conducting substrate. The layered kernels are computed directly for controllable accuracy. The proposed methods are validated against existing methods for both electromagnetic and electromagnetic-circuit problems.