Treatment of complete loss of skin thickness requires expensive cellular materials and limited skin grafts used as temporary coverage. This paper presents an acellular bilayer scaffold modified with polydopamine (PDA), which is designed to mimic a missing dermis and a basement membrane (BM). The alternate dermis is made from freeze-dried collagen and chitosan (Coll/Chit) or collagen and a calcium salt of oxidized cellulose (Coll/CaOC). Alternate BM is made from electrospun gelatin (Gel), polycaprolactone (PCL), and CaOC. Morphological and mechanical analyzes have shown that PDA significantly improved the elasticity and strength of collagen microfibrils, which favorably affected swelling capacity and porosity. PDA significantly supported and maintained metabolic activity, proliferation, and viability of the murine fibroblast cell lines. The in vivo experiment carried out in a domestic Large white pig model resulted in the expression of pro-inflammatory cytokines in the first 1–2 weeks, giving the idea that PDA and/or CaOC trigger the early stages of inflammation. Otherwise, in later stages, PDA caused a reduction in inflammation with the expression of the anti-inflammatory molecule IL10 and the transforming growth factor β (TGFβ1), which could support the formation of fibroblasts. Similarities in treatment with native porcine skin suggested that the bilayer can be used as an implant for full-thickness skin wounds and thus eliminate the use of skin grafts.