Recently, the biomedical scientists who are working in the skin regeneration area have proposed asymmetric membranes as ideal wound dressings, since they are able to reproduce both layers of skin and improve the healing process as well as make it less painful. Herein, an electrospinning technique was used to produce new asymmetric membranes. The protective layer was composed of a blending solution between polycaprolactone and polylactic acid, whereas the underlying layer was comprised of methacrylated gelatin and chitosan. The chemical/physical properties, the in vitro hemo- and biocompatibility of the nanofibrous membranes were evaluated. The results obtained reveal that the produced membranes exhibited a wettability able to provide a moist environment at wound site. Moreover, the membranes’ hemocompatibility and fibroblast cell adhesion, spreading and proliferation at the surface of the membranes were also noticed in the in vitro assays. Such results highlight the suitability of these asymmetric membranes for wound dressing applications.