We prepared a simple, low-cost membrane suitable for gravity-driven oil-water separation and water purification. Composite membranes with selective wettability were fabricated from a mixture of aqueous poly(diallyldimethylammonium chloride) solution, sodium perfluorooctanoate, and silica nanoparticles. Simply dip-coating a stainless steel mesh using this mixture produced the oil-water separator. The contact angles (CAs) of hexadecane and water on the prepared composite membranes were 95 +/- 2 degrees and 0 degrees, respectively, showing the oleophobicity and superhydrophilicity of the membrane. In addition, a graphene plug was stacked below the membrane to remove water-soluble organics by adsorption. As a result, this multifunctional device not only separates hexadecane from water, but also purifies water by the permeation of the separated water through the graphene plug. Here, methylene blue (MB) was removed as a demonstration. Membranes were characterized by high-resolution scanning electron microscopy (HRSEM), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), and Fourier transform infrared (FT-IR) spectroscopy to elucidate the origin of their selective wettability.