In this study, lemon balm (Melissa officinalis L.) and dill (Anethum graveolens L.) essential oils (EOs) were encapsulated into collagen hydrolysates extracted from bovine tendons and rabbit skins, both mixed with chitosan (CS) by using the coaxial electrospinning technique for potential wound dressing applications. The morphology and chemical composition of the electrospun nanofibers were investigated using scanning electron microscopy (SEM) and attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR). The antimicrobial activity of the dill EO and lemon EO, as well as the electrospun samples loaded with essential oils was determined by disk diffusion assay against Staphylococcus aureus ATCC 25923, Escherichia coli ATCC 25922, Enterococcus faecalis ATCC 29212, and Salmonella typhimurium ATCC 14028 bacterial strains; Candida albicans ATCC 10231 and Candida glabrata ATCC 90028 yeast strains; and Aspergillus brasiliensis ATCC 9642 fungal strain. In vivo biocompatibility testing of the collagen hydrolysate-chitosan/essential oil electrospun nanofibers was based on the determination of the hematological, biochemical, and immunological profile and the evaluation of the influence produced on the oxidative stress in white Swiss mice. The synergetic effect of dill and lemon balm EOs can improve the antimicrobial activity of collagen hydrolysate-chitosan nanofibers against the most important bacterial strains. The in vivo test results suggested a good biocompatibility of electrospun samples based on collagen hydrolysate extracted from bovine tendons or rabbit skin mixed with chitosan and containing dill and/or lemon balm essential oils as encapsulated bioactive compounds.