To investigate the impermeability characteristics of composite geomembranes in rigid landfills, a three-dimensional finite element seepage analysis model, which incorporates a composite geomembrane, was established based on a case study of a rigid landfill project in Tongling. Utilizing the seepage mechanism of the composite geomembrane, the seepage distribution patterns of the hazardous waste leachate within the unit cell were computed under representative operating conditions. Different thickness amplification factor schemes for the equivalent treatment of the composite geomembrane were comparatively analyzed, considering both isotropic and anisotropic seepage conditions. The relationships between the seepage flow rate, velocity, and thickness amplification factor were determined. The results showed that the leachate experiences a rapid drop in the water head as it passes through the composite geomembrane, with a low seepage flow rate and velocity, highlighting the membrane’s significant impermeability effect. The finite element analysis indicated that thickness amplification of the composite geomembrane based on the flow equivalence is feasible to some degree, but treating the geomembrane as an anisotropic material during the equivalent process better approximates the actual conditions.