Upregulation of vascular endothelial growth factor A/basic fibroblast growth factor (VEGFA/bFGF) expression in the penumbra of cerebral ischemia can increase vascular volume, reduce lesion volume, and enhance neural cell proliferation and differentiation, thereby exerting neuroprotective effects. However, the beneficial effects of endogenous VEGFA/bFGF are limited as their expression is only transiently increased. In this study, we generated multilayered nanofiber membranes loaded with VEGFA/bFGF using layer-by-layer self-assembly and electrospinning techniques. We found that a membrane containing 10 layers had an ideal ultrastructure and could efficiently and stably release growth factors for more than 1 month. This 10-layered nanofiber membrane promoted brain microvascular endothelial cell tube formation and proliferation, inhibited neuronal apoptosis, upregulated the expression of tight junction proteins, and improved the viability of various cellular components of neurovascular units under conditions of oxygen/glucose deprivation. Furthermore, this nanofiber membrane decreased the expression of Janus kinase-2/signal transducer and activator of transcription-3 (JAK2/STAT3), Bax/Bcl-2, and cleaved caspase-3. Therefore, this nanofiber membrane exhibits a neuroprotective effect on oxygen/glucose-deprived neurovascular units by inhibiting the JAK2/STAT3 pathway.