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This study develops a two-domain physics-informed neural network framework for contaminant transport through a GCL/SL composite liner system, in which the thin GCL layer is treated using a steady-state advection-dispersion-biodegradation formulation and the underlying soil liner is modeled as a transient transport domain. Two formulations are evaluated against analytical and finite-element reference solutions under different leachate-head conditions: a standard PINN with soft constraint enforcement (Std-PINN) and a hard-constrained PINN (H-PINN), in which selected boundary and initial conditions are embedded directly into the trial solutions. The Std-PINN captures the overall breakthrough behavior but shows larger errors during the early transport stage, particularly under higher leachate heads where advective transport becomes more pronounced. The H-PINN reduces the optimization burden associated with penalty-based constraint enforcement and provides more accurate and stable concentration predictions, lowering the MAE from approximately 0.058-0.067 for the Std-PINN to about 0.011-0.023 for the H-PINN, while reducing the MRE from approximately 9.10%-19.16% to about 2.08%-3.14%. Parametric analyses confirm that the H-PINN with the tanh activation function and an optimized network structure provides the best predictive accuracy. The H-PINN is further extended to inverse modeling for identifying the SL degradation half-life from limited concentration observations, showing reliable convergence toward prescribed values and acceptable robustness under low-to-moderate observation noise.