Organic-aqueous liquid (phenol) extraction is one of many standard techniques to efficiently purify DNA directly from cells. Effective dispersion of one fluid phase in the other increases the surface area over which biological component partitioning may occur, and hence enhances DNA extraction efficiency. Electrohydrodynamic (EHD) instability can be harnessed to achieve this goal and has been experimentally demonstrated by one of the co-authors (JDZ). In this work, analysis and simulation are combined to study two-phase EHD instability. In the problem configuration, the organic (phenol) phase flows into the microchannel in parallel with and sandwiched between two aqueous streams, creating a three-layer planar geometry; the two liquid phases are immiscible. An electric field is applied to induce instability and to break the organic stream into droplets. The Taylor-Melcher leaky-dielectric model is employed to investigate this phenomenon. A linear analysis is carried out with a Chebyshev pseudospectral method, whereas a fully nonlinear numerical simulation is implemented using a finite volume, immersed boundary method (IBM). The results from both models compare favorably with each other. The linear analysis reveals basic instability characteristics such as kink and sausage modes. On the other hand, the nonlinear simulation predicts surface deformation in the strongly nonlinear regime pertinent to droplet formation. These numerical tools will be used to investigate the effects of the applied electric field, geometry, and convective flow rate on mixing and dispersion. The eventual objective is to maximize surface area of the organic phase under given experimental conditions for optimized DNA extraction.