Thin porous layers, that have large aspect ratios, are seen in many applications such as hydrogen fuel cells and hygiene products, in which air-water immiscible flow is of great interest. Direct numerical simulations based on Navier-Stokes equation are computationally expensive, and even prohibitive for low capillary number flow such as water flooding in low-temperature polymer electrolyte fuel cells. Alternatively, the pore-network modeling needs much less computational resources, while still retaining essentials of the pore-structure information. In this work, a dynamic pore-network model of air-water flow with phase change has been developed. We focus on drainage processes through thin porous layers, in which liquid water is the nonwetting phase. Three test cases are conducted, namely, air-water flow through a thin porous layer, air-water flow through a bilayer of fine and coarse thin porous layers, and water flooding in the gas diffusion layer of a polymer electrolyte fuel cell with phase change between water and its vapor. Using these test cases, we aim to demonstrate the application of dynamic pore-network modeling in thin porous media studies. In particular, we discuss the challenge of modeling thin porous media at the average scale, and highlight the role of phase change in removing liquid water from the cathode gas diffusion layer.