We report the dynamics of aqueous droplets of different size and viscosity at the interface of a coflowing stream of immiscible oils (i.e., primary and secondary continuous phases) in a microchannel, at low Re. The lateral migration of droplets introduced into the primary continuous phase toward the interface and subsequent selective migration of droplets across the interface into the secondary continuous phase is investigated. The interplay between the competing noninertial lift and interfacial tension forces, which govern the interfacial migration of the droplets, is presented and discussed. The velocity and strain rate profiles, and interface location, which are critical for calculating the lift force and migration behavior of droplets, are presented. The trajectories of droplets of different size and viscosity in the primary continuous phase are obtained for different interface locations. During interfacial migration, the deformation behavior of droplets of different viscosities is studied. Finally, sorting of droplets based on size contrast is demonstrated and sorting efficiency is found. A new paradigm of migration and sorting of droplets is reported, which could find importance in chemical and biological applications. © 2016 American Chemical Society.