We demonstrate the significantly enhanced molecular separation performance of stacked graphene oxide nanoribbon (GONR) membranes with a carbon nanotube (CNT) supporting layer. Functionalized CNTs (FCNTs) are prepared for the bilayer membrane by partially oxidizing CNTs with KMnO₄, which can be dispersed in various solvents and water up to 40 mg/mL without the addition of a surfactant. The concentrated FCNT dispersion is viscous and can be coated on porous polymeric support using a scalable bar-coating method. When a selective GONR layer is vacuum filtrated onto the FCNT-coated support, the membrane can filter organic dye molecules with a 100% rejection rate, while allowing fast penetration of small ions and water, resulting in an excellent diafiltration performance with a separation factor of 950 and water flux of 138 LMH. Due to the strong adhesion of FCNTs and GONRs on polymeric support, the membrane can be operated at high pressures (up to 30 bar) and under continuous cross-flow conditions.