The 2019 coronavirus outbreak and worsening air pollution have triggered the search for manufacturing effective protective masks preventing both particulate matter and biohazard absorption through the respiratory tract. Therefore, the design of advanced filtering textiles combining efficient physical barrier properties with antimicrobial properties is more newsworthy than ever. The objective of this work was to produce a filtering electrospun membrane incorporating a biocidal agent that would offer both optimal filtration efficiency and fast deactivation of entrapped viruses and bacteria. After the eco-friendly electrospinning process, polyvinyl alcohol (PVA) nanofibers were stabilized by crosslinking with 1,2,3,4-butanetetracarboxylic acid (BTCA). To compensate their low mechanical properties, nanofiber membranes with variable grammages were directly electrospun on a meltblown polypropylene (PP) support of 30 g/m2. The results demonstrated that nanofibers supported on PP with a grammage of around only 2 g/m2 presented the best compromise between filtration efficiencies of PM0.3, PM0.5, and PM3.0 and the pressure drop. The filtering electrospun membranes loaded with benzalkonium chloride (ADBAC) as a biocidal agent were successfully tested against E. coli and S. aureus and against human coronavirus strain HCoV-229E. This new biocidal filter based on electrospun nanofibers supported on PP nonwoven fabric could be a promising solution for personal and collective protection in a pandemic context.