This work presents a systematic study of the influence of membrane–solvent–solute interactions on the permeation performance of solvent resistant nanofiltration (NF) membranes. Two different tailor-made composite membranes are prepared by dip coating of a polymer onto a polyacrylonitrile (PAN) support: a hydrophobic (using polydimethylsiloxane (PDMS) polymer) and a new hydrophilic (using polyethylene oxide (PEO)–PDMS–PEO tri-block copolymer). The transport of various pure solvents through the PAN/PDMS and PAN/PEO–PDMS–PEO composite membranes is studied showing a reasonably linear relation between the solvent permeability and the ratio of membrane swelling/solvent viscosity. For the transport of sunflower oil/toluene mixtures through the PAN/PDMS composite membrane, the “apparent” viscosity inside the membrane and the membrane swelling seem to be the main parameters affecting the toluene transport. The oil/toluene system is ideal. Osmotic phenomena are observed which can be interpreted by the van’t Hoff osmotic pressure model. Furthermore, flux coupling between oil and toluene is significant resulting in rather moderate oil retention by the membrane (70–80%). The coupling between oil/toluene is stronger than between oil/hexane. For the transport of tetraoctylammonium bromide (TOABr)/toluene mixtures through the PAN/PDMS membrane the phenomena are more complex. The system is non-ideal and no osmotic phenomena are observed. This can be correlated with the formation of ion-pairs of TOABr in toluene. Furthermore, the concentration polarization phenomena are significant resulting in low toluene fluxes and 100% retention of TOABr by the membrane.