In the field of tissue engineering, the use of core-shell fibers represents an advantageous approach to protect and finely tune the release of bioactive compounds with the aim to regulate their efficacy. In this work, core-shell electrospun polycaprolactone nanofiber-based membranes, loaded with rifampicin and coated with silver nanoparticles, were developed and characterized. The membranes are composed by randomly oriented nanofibers with a homogeneous diameter, as demonstrated by scanning electron microscopy (SEM). An air-plasma treatment was applied to increase the hydrophilicity of the membranes as confirmed by contact angle measurements. The rifampicin release from untreated and air-plasma treated membranes, evaluated by UV spectrophotometry, displayed a similar and constant over-time release profile, demonstrating that the air-plasma treatment does not degrade the rifampicin, loaded in the core region of the nanofibers. The presence and the distribution of silver nanoparticles on the nanofiber surface were investigated by SEM and Energy Dispersive Spectroscopy. Moreover, SEM imaging demonstrated that the produced membranes possess a good stability over time, in terms of structure maintenance. The developed membranes showed a good biocompatibility towards murine fibroblasts, human osteosarcoma cells and urotheliocytes, reveling the absence of cytotoxic effects. Moreover, doble-functionalized membranes inhibit the growth of E. coli and S. aureus. Thanks to the possibilities offered by the coaxial electrospinning, the membranes here proposed are promising for several tissue engineering applications.