Membrane fouling is a major drawback in the membrane filtration industry for water treatment. Mixed-matrix membranes (MMMs) are well known for their enhanced antifouling and antibacterial properties, which could offer potential benefits for membrane filtration processes in the water treatment field. In this work, three electrospun nanofibrous MMMs (P, CP, and MCP, which were, respectively, the pristine polysulfone membrane and mixed-matrix membranes (MMMs) consisting of GO–ZnO and GO–ZnO–iron oxides) were studied for antifouling and antibacterial properties with respect to the arsenic nanofiltration process. The effects of these composites on the antifouling behaviour of the membranes were studied by characterising the bovine serum albumin (BSA) protein adsorption on the membranes and subsequent analysis using microscopic (morphology via scanning electron microscopy) and Brunauer–Emmett–Teller (BET) analyses. The antibacterial properties of these membranes were also studied against Gram-positive Staphylococcus aureus (S. aureus) and Gram-negative Escherichia coli (E. coli). The composite nanoparticle-incorporated membranes showed improved antifouling properties in comparison with the pristine polysulfone (PSF) membrane. The excellent antimicrobial properties of these membranes make them appropriate candidates to contribute to or overcome biofouling issues in water or wastewater treatment applications.