This work reports the construction of a bicomponent scaffold co-loaded with both a prodrug and a drug (BiFp@Ht) as an efficient platform for wound dressing, by combining the electrospinning and 3D-printing technologies. The outer component consisted of a chitosan/polyethylene oxide-electrospun membrane loaded with the indomethacin–polyethylene glycol–indomethacin prodrug (Fp) and served as a support for printing the inner component, a gelatin methacryloyl/sodium alginate hydrogel loaded with tetracycline hydrochloride (Ht). The different architectural characteristics of the electrospun and 3D-printed layers were very well highlighted in a morphological analysis performed by Scanning Electron Microscopy (SEM). In vitro release profile studies demonstrated that both Fp and Ht layers were capable to release the loaded therapeutics in a controlled and sustained manner. According to a quantitative in vitro biological assessment, the bicomponent BiFp@Ht scaffold showed a good biocompatibility and no cytotoxic effect on HeLa cell cultures, while the highest proliferation level was noted in the case of HeLa cells seeded onto an Fp nanofibrous membrane. Furthermore, the BiFp@Ht scaffold presented an excellent antimicrobial activity against the E. coli and S. aureus bacterial strains, along with promising anti-inflammatory and proangiogenic activities, proving its potential to be used for wound dressing.