We developed composite membranes by stacking functionalized nanospheres (20 nm size) with a high density of H-bonds. The functionalized nanospheres were formed by a click-reaction in toluene between the polybutadiene segment of poly(styrene-b-butadiene-b-styrene) (PS-b-PB-b-PS) triblock copolymer and an azodicarbonyl (PTAD) compound. The strong hydrogen-bond interaction promoted by the pendant urazole groups of the PTAD-modified copolymer is an important parameter for obtaining stable and defect-free membranes, acting in analogy to self-healing systems. The hydrodynamic transport is facilitated by the high porosity of the membranes and the unique hourglass-shaped pores. The composite membrane has water permeation as high as 60 Lm−2 h−1 bar−1 and can exclude more than 95% of proteins with a molecular weight as small as 12 kg mol−1. This novel class of nanoparticle-stacked membranes has therefore excellent separation properties for biomolecular separation.