High-performance pervaporation membranes have potential in industrial separation applications, but overcoming the permeability-selectivity trade-off is a challenge. We report a strategy to create highly flexible metal-organic framework nanosheet (MOF-NS) membranes with a faveolate structure on polymer substrates for alcohol-water separation. The controlled growth followed by a surface-coating method effectively produced flexible and defect-free superhydrophobic MOF-NS membranes. The reversible deformation of the flexible MOF-NS and the vertical interlamellar pathways were captured with electron microscopy. Molecular simulations confirmed the structure and revealed transport mechanism. The ultrafast transport channels in MOF-NS exhibited an ultrahigh flux and a separation factor of 8.9 in the pervaporation of 5 weight % ethanol-water at 40°C, which can be used for biofuel recovery. MOF-NS and polydimethylsiloxane synergistically contribute to the separation performance.