We inject water at a low flow rate through gas diffusion layers containing different percentages of polytetrafluoroethylene (PTFE) coating: 5, 20, 40, and 60%. We use high-resolution three-dimensional X-ray imaging to identify the arrangement of fibers, water, and air in the pore space. We also quantify the contact angle and meniscus curvature once the water has spanned the layer, flow has ceased, and water has reached a position of equilibrium. The average contact angle and water pressure at breakthrough increase with the amount of coating, although we see a wide range of contact angles with values both above and below 90°, indicating a mixed-wet state. We identify that the menisci form minimal surfaces (interfaces of zero curvature) consistent with pinned gas-water-solid contacts. Scanning electron microscopy images of the fibers show that the coated fibers have a rough surface. Between 93 and 100% of the contacts identified were found on the rough, hydrophobic, coated fibers or at the boundary between uncoated (hydrophilic) and coated (hydrophobic) regions; we hypothesize that these contacts are pinned. The one exception is the 60% PTFE layer, which shows distinctly hydrophobic properties and a negative capillary pressure (the water pressure is higher than that of air). The presence of minimal surfaces suggests that the water and gas pressures are equal, allowing water to flow readily without pressure build-up. From topological principles, the negative Gaussian curvature of the menisci implies that the fluid phases are well connected. The implication of these results is explored for the design of porous materials where the simultaneous flow of two phases occurs over a wide saturation range.