Thin artificial surfaces that act as high frequency bandgap structures have been recently studied for the design of gap waveguides, hard surfaces, and planar lenses. Here, we propose a circuit-based method to analyze glide-symmetric corrugated metasurfaces that are embedded in a thin parallel plate waveguide. Our closed-form solution is based on rigorous analytical derivations. It achieves remarkable agreement with full-wave solvers, even when the waveguide thickness is extremely thin. In contrast, classical homogenization approaches are shown to be inaccurate for thin waveguides due to the interaction of higher order Floquet modes between the surfaces. Numerical results validate our theoretical analysis and show the utility of the proposed method.