Skin wound healing is a complex physiological process that involves various cell types, growth factors, cytokines, and other bioactive compounds. In this study, a novel dual-function multilayered nanofibrous membrane is developed for chronic wound application. The membrane is composed of five alternating layers of polycaprolactone (PCL) and poly (vinyl alcohol) (PVA) nanofibers (PCL-PVA) with a dual function: the PCL nanofibrous layers allow cell adhesion and growth, and the PVA layers enriched with incorporated platelet lysate (PCL-PVA + PL) serve as a drug delivery system for continuous release of bioactive compounds from PL into an aqueous environment. The material is produced using a needleless multi-jet electrospinning approach which can lead to homogeneous large-scale production. The bioactive PCL-PVA + PL membranes are cytocompatible and hemocompatible. A spatially compartmented co-culture of three cell types involved in wound healing - keratinocytes, fibroblasts and endothelial cells - is used for cytocompatibility studies. PCL-PVA + PL membranes enhance the proliferation of all cell types and increase the migration of both fibroblasts and endothelial cells. The membranes are also hemocompatible without any deleterious effect for thrombogenicity, hemolysis and coagulation. Thus, the beneficial effect of the PCL-PVA + PL membrane is demonstrated in vitro, making it a promising scaffold for the treatment of chronic wounds.