Laterally stratified fully developed flow in a curved channel is investigated, in this work. Motivated by applications in microchannels, we focus on the limit of small Reynolds numbers. The method of domain perturbation is used to obtain an analytical solution, by considering the curvature ratio of the channel (ratio of the channel's width to its radius of curvature) to be a small parameter. Centrifugal forces give rise to multiple pairs of Dean vortices in the two fluids. Depending on the properties of the fluids and their holdups (volume fractions), one of the fluids dominates the flow and influences the flow pattern within the other fluid. The multi-dimensional parameter space is divided into five different regions, each characterized by a distinct vortex pattern. Centrifugal forces are shown to deform the interface; it bulges outward, in the direction of centrifugal force, to an extent that increases with the Weber number (ratio of centrifugal forces to interfacial tension forces). The deformation also depends on the flow pattern. Redistribution of the axial velocity profile is analyzed and attributed to geometric and inertial effects. The perturbation solution is compared with numerical simulations and found to be accurate for the range of Reynolds numbers and curvature ratios typically encountered in microchannel applications. (C) 2015 Elsevier Ltd. All rights reserved.