Effective oil/water separation and removal of organic molecules from water are of worldwide importance for water source protection. Multifunctional sorbent materials with excellent sorption capacity, stability, and recyclability properties need to be developed. Here, flexible and multifunctional polymer/porous boron nitride nanosheets (BNNSs) membranes with high water permeability, exhibiting high effectiveness and stability in the purification of simulated wastewater tainted with either oil/water emulsion or organic molecules, are reported. Remarkably, the flexible nature of these porous membranes enables simplicity of operation for water remediation processing and ease of post-processing collection. The composite membrane also displays a remarkably high permeability of 8 × 104 L μm m-2 h-1 bar-1, roughly three orders of magnitude higher than pure polymer, and excellent filter efficiencies for the pharmaceuticals ciprofloxacin, chlortetracycline, and carbamazepine (up to 14.2 L g-1 of BNNSs in the composite membrane for a concentration of 10 mg L-1 ciprofloxacin) and the dye methylene blue (up to 9.3 L g-1 of BNNSs in the composite membrane at a concentration of 30 mg L-1). Exhausted membranes can be readily rejuvenated by simple washing with retention of their high-performance characteristics. The results demonstrate the potential efficacy and practicality of these membranes for water cleaning.