Here, we propose an efficient and simple approach for the analysis of electromagnetic interaction at microwave and terahertz frequencies with multilayer metasurfaces formed by stacking periodic arrays of metallic (and complementary) subwavelength inclusions in dielectric environment. The analysis is based on the concepts from circuit theory of the entire bulk 3-D structure, wherein the surface impedance (admittance) of canonical metasurfaces (patch arrays, fishnets, Jerusalem cross arrays, and others) has been obtained in closed form from the scattering problem. It has been demonstrated that a fishnet-dielectric stack enables an enhanced transmission at microwave and terahertz frequencies, mimicking a similar resonance behavior observed with a metal-dielectric stack at optical frequencies. Recently, this idea has been elevated to the use of graphene at low-terahertz frequencies, and it has been demonstrated that a stack of graphene monolayers behaves similar to that of the multilayer fishnets in microwave and terahertz regimes. Also, we have observed that periodic graphene nano-patches at low-terahertz possess dual capacitive-inductive nature combining low-pass and high-pass characteristics of metallic (patch array) and complementary (fishnet) periodic arrays.