Modern medical treatment can be improved by nanotechnology methods for preparing nanocomposites with novel physical, chemical and biological properties. The materials studied and analysed as membranes were produced from poly(ε-caprolactone) (PCL), which contained identical amounts of nano-additives, either montmorillonite (MMT) or functionalized multi-walled carbon nanotubes (MWCNT-f), while the reference membranes were obtained from unmodified PCL. In addition to the conventional methods used in the study of materials for medical purposes such as DSC, contact angle measurements, surface topography, Raman spectroscopy was also applied. Raman microspectroscopy can decode the phenomenon that occurs in the polymer in contact with the nanoparticles. Besides identifying the vibrations of certain functional groups, the calculation of crystallinity parameters is also possible, by which the most intense interactions within the nanocomposites can be analysed. The Raman studies indicate that each of the nano-additives reacts differently with the polymer matrix, which results in material properties that influence its biological properties. MWCNT-f interacts preferentially with the oxygen-containing groups, and particularly with the backbone regions in the vicinity of the single CO bond. The human osteoblast-like MG-63 cells, cultured on the PCL/MWCNT-f membrane for three days, show almost 100% viability.