Polycaprolactone (PCL) and PCL/gelatin membranes and films were fabricated by electrospinning and solvent casting. A systematic analysis of the morphology evolution, as degradation occurred, was made to separate the contribution of fiber nanotexture and gelatin biochemical signal on cell adhesion and proliferation. Field emission scanning electron microscope was used to assess the contribution of platform architecture on the gelatin degradation by the morphological changes that occurred at different times. The evaluation of human mesenchymal stem cells' biocompatibility confirmed the role of architecture and chemical composition on cell response. The nanostructured surfaces positively affected the cell recognition by increasing the surface area. The gelatin embedded in the PCL matrix of the nanofibers improved the cell/material interaction and provided support to the proliferation. The PCL/gelatin electrospun membranes showed an increase in mineralization when conditioned in osteogenic medium; this system has promise for long-term in vitro investigations of bone regeneration.