Electrospinning of a segmented copolymer having polyglycolide hard segments is successfully performed from 1,1,1,3,3,3-hexafluoroisopropanol solutions. During the process, a bactericidal agent, i.e., chlorhexidine (CHX), is effectively loaded, which results in nanofibers with a smaller diameter because of the change in solution conductivity. New fabrics based on molding of alternate layers of poly(ε-caprolactone) (PCL) films and the electrospun scaffolds of the segmented copolymer are prepared and characterized. The thermal molding process renders a PCL matrix homogeneously reinforced with nanofibers that compensate for the loss of mechanical properties caused by incorporation of CHX. Release of CHX is evaluated in different media. Results vary depending on the layer where the drug is incorporated. Thus, systems with an immediate bacteriostatic effect, as well as systems with a potential long term antimicrobial effect, are obtained. Growth inhibition and adhesion assays demonstrate the fast bactericidal effect of samples with CHX loaded in its outer layers.