Superomniphilic materials are defined as materials that can uptake both water and oil-like liquids. In this study, a facile method to prepare a superomniphilic and biodegradable core-shell structure of poly(glycerol sebacate) (PGS) and poly(L-lactic acid) (PLLA) is reported. The developed method immobilizes the PGS polymer onto the surface of the PLLA electrospun fibers, increasing the presence of hydroxyl groups on the surface of the membranes. The sample with 25 wt% PGS can uptake polar and apolar solvents, and presents a superhydrophilic behavior. The PGS-PLLA composite is reusable up to 10 cycles of solvent (water of organic solvents) absorption with a separation efficiency of 99.5%, and its general appearance resembles the first absorption/compression cycle. Finally, this work presents a novel biodegradable polymeric blend membrane with superomniphilic properties, produced by a scalable process, which could be easily implemented to fight against environmental disasters such as large area oil spills.