This study presents an analytical model for two-dimensional pollutant transport within a three-layer composite liner system, which comprises a geomembrane (GM), a geosynthetic clay liner (GCL), and a soil liner (SL), with particular attention to defects in the geomembrane. The model integrates key processes such as convection, diffusion, adsorption, and degradation, offering a more accurate prediction of pollutant behavior. Through Laplace and Fourier transforms, pollutant concentration distributions are derived, providing a comprehensive view of pollutant migration in landfill settings. Verification against COMSOL 6.0 simulations underscores the model’s robustness. Results show that there is an optimal thickness for the SL that balances the effectiveness of pollutant containment and material usage, while higher diffusion coefficients and advection velocity accelerate migration. The degradation of organic pollutants reduces concentrations over time, especially with shorter half-lives. These findings not only improve the design of landfill liners but also support more sustainable waste management practices by reducing the risk of environmental contamination. This research contributes to the development of more effective, long-lasting landfill containment systems, enhancing sustainability in waste management infrastructure.