Neutron radiography, a non-destructive imaging technique, is applied to study water and solute transport through desalination membranes. Specifically, we use neutron radiography to quantify lithium chloride draw solute concentrations across a thin-film composite membrane during forward osmosis permeation. This measurement provides direct visual confirmation of incomplete support layer wetting and reveals significant dilutive external concentration polarization of the draw solution outside of the membrane support layer. These transport-limiting phenomena have been hypothesized in previous work and are not accounted for in the standard thin-film model of forward osmosis permeation, resulting in inaccurate estimations of membrane transport properties. Our work demonstrates neutron radiography as a powerful measurement tool for studying membrane transport and emphasizes the need for direct experimental measurements to refine the forward osmosis transport model.