A frequency-domain multi-solver domain decomposition method is presented to accurately analyze signal integrity problems in multi-scale integrated circuits. In particular, we propose a novel formulation to rigorously account for the conductor loss due to finite conductivities in metals. The proposed non-conformal domain decomposition method follows a hierarchical domain partitioning strategy of the original problem. The most suitable computational electromagnetic technique is employed for each of the subregions. To improve the convergence in the DDM iterations, an optimized Robin type transmission condition is introduced to enforce the field continuities across sub-domain interfaces. Moreover, a hierarchical multi-level fast multiple method is adopted to address the low frequency issues particularly in IC applications. Rigorous numerical experiments validate the potential efficiency and benefits offered by the proposed method.