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The partial-element equivalent-circuit (PEEC) method is generalized to include multilayer dielectric interfaces. The boundary between two different dielectrics is treated as a new region to develop an interface Green's function. The interface Green's function is subsequently used to calculate the capacitances and inductances of interface surface cells. The method is first verified, using a microstrip to evaluate the quasi-static capacitance, with the method of Wheeler. It is then extended to the PEEC formulation and applied to coupled microstrip-line filter with multilayered dielectrics. The results are compared with that of the method of moments. Agreement is found in the prediction of resonant frequencies and S-parameters.