When a range of lipid bilayers are melted to the disordered fluid phase from the (much less permeable) ordered gel phase, their permeability to a variety of permeants shows a peak at the transition temperature and drops off with increasing temperature, rather than just rising as melting proceeds. To explore this anomalous behavior, a simulated coarse-grained lipid membrane model that exhibits a phase transition upon expansion or compression was studied to determine how the permeation rate of a simple particle depends on the phase composition in the two-phase region and on particle size. The permeation rate and each phases area fraction and area density could be directly calculated, along with the probability that the permeant would cross in either phase or in interfacial regions. For large permeants and system sizes, conditions could be found where permeability increases upon compression of the bilayer. Permeation was negligible in the gel phase and, in contrast to the predictions of the "leaky interface" hypothesis, was not enriched in interfacial regions. The anomalous effect could instead be attributed to an increase in the area per lipid of fluid-phase domains. This result motivated a model for the decrease in effective permeability barrier through fluid-phase domains arising from a decrease in the length of the gel/fluid interface at the midpoint of a permeation event.