In this work, we develop low-dimensional models to describe steady-state mass transfer and reactions in two-phase stratified flow in microchannels. The partial differential equations that consider the effect of axial convection, transverse diffusion, and reaction are averaged in the transverse direction using the Lyapunov Schmidt method. The resulting reduced-order model describes the evolution of the cup-miming average and cross-section average concentrations along the axial direction. Two different reduced models are obtained: a One-Equation-Averaged (OEA) model, in which we average across both fluids simultaneously, and a Two-Equation-Averaged (TEA) model, in which we average across each fluid separately by embedding in a family of cognate problems. The OEA model cannot capture the initial mass transfer between the phases when they first come into contact at the inlet of the channel. It can only be used when there is a deviation from equilibrium due to a reaction. The TEA model overcomes these limitations and is able to describe mass transfer between the phases right from the inlet of the channel. It accurately predicts extraction and reactive extraction with slow reactions. However, if the reaction is fast, the TEA model fails and the OEA model is preferable. Some applications of the TEA model are presented. It leads to closed-form expressions for the overall mass-transfer coefficient, in terms of the properties of the fluids and their holdups. An analytical solution of the TEA model is derived for the case of nonreactive extraction and is used to identify the operating conditions for high extraction performance. Finally, the TEA model is applied to investigate how the yield in competitive-consecutive reactions can be improved by exploiting the mass-transfer resistance between the two phases.