Environmentally friendly membranes with on-demand oil/water separation ability have recently received increasing attention in the application field of oily wastewater treatment. Herein, a facile and sustainable approach to prepare a flexible electrospun nanofiber/nanonet membrane using biodegradable polymers, chitosan (CS), and polycaprolactone (PCL) for controllable oil/water separation was demonstrated. The CS@PCL membranes are superamphiphilic, with both water and oil contact angles in air of 0°. The CS@PCL membrane shows underoil superhydrophobicity and underwater superoleophobicity. The membrane can effectively separate various oil/water mixtures, including immiscible oil/water mixtures and oil-in-water and water-in-oil emulsions by a simple prewetting approach. The obtained membrane exhibits a high separation efficiency of above 94.6% for immiscible light/heavy oil/water mixtures. Furthermore, the membrane shows excellent separation efficiencies for oil-in-water emulsions and water-in-oil emulsions, as above 99.9 and 94.5%, respectively.