Ionic conductivity in a polymeric fuel cell requires water uptake. Previous theoretical studies of water uptake used idealized parameters. We report a parameter-free prediction of the water-swelling behavior of a model fuel cell membrane. The model polymers, poly(methyl-butylene)-block-poly(vinylbenzyl-trimethylamine), form lamellar domains that absorb water in humid air. We use the Scheutjens-Fleer methodology to predict the resulting change in lamellar structure and compare with x-ray scattering. The results suggest locally uniform water distributions. However, under conditions where a PVBTMA and water mixture phase-separate, the two phases arrange into stripes with a dilute stripe sandwiched between two concentrated stripes. A small amount of water enhances conductivity most when it is partitioned into such channels, improving fuel-cell performance.