Multiphase flow control is a challenging task in microfluidic systems. Application of such ideas in electroosmotic actuation of multiphase flows, which involves a complex convolution of phenomena ranging from electrochemistry to hydrodynamics, is even more tricky. Most of the existing studies in the field have limited their scope to the thin electric double layer (EDL) limit, where the role of ionic space charge distribution in the EDL is simplified to provide a slip velocity boundary condition at the substrate, and the role of the fluid-fluid interface is limited to continuity of velocity and hydrodynamic shear stress. In this study, electro-osmotic flow of two immiscible fluids, an electrolytic solution and an inert gas, are studied in a rectangular microchannel and the role of interfacial potential and Maxwell stress-generated dynamics is explored in a wide range of EDL thicknesses. A net stress term is used in the transport equations which includes the electric effects by Maxwell stress as well as the hydrodynamic stress. It is observed that the free surface, depending upon its potential may enhance the fluid velocity or act as a rigid wall. With the help of two-dimensional velocity contour plots, the role of various flow parameters on flow profile is discussed. Further, a parametric analysis of flow rate gives interesting insights into the flow rate reversal and control in such microfluidic devices.