A multilayer nanofibrous membrane consisting of a layer of polycaprolactone and one of physically cross-linked alginate-embedding ZnO nanoparticles is prepared via electrospinning technique as potential wound healing patches with drug delivery capabilities. A washing-cross-linking protocol is developed to obtain stable materials at the same time removing poly(ethylene oxide), which was used here as a cospinning agent for alginate, without interfering with the membrane's peculiar nanofibrous structure. The mechanical behavior of the samples is assessed via a uniaxial tensile test showing appropriate resistance and manageability together with a good thermal stability as proved via thermogravimetric analysis. The polycaprolactone external layer enriches the samples with good liquid-repellent properties, whereas the alginate layer is able to promote tissue regeneration owing to its capability to promote cell viability and allow exudate removal and gas exchanges. Moreover, using methylene blue and methyl orange as model molecules, promising drug delivery abilities are observed for the mats. Indeed, depending on the nature and on the dye-loading concentration, the release kinetic can be easily tuned to obtain a slow controlled or a fast burst release. Consequently, the proposed alginate-polycaprolactone membrane represents a promising class of innovative, simple, and cost-effective wound healing patches appropriate for large-scale production.