Membranes based on poly(ε-caprolactone)/poly(3-hydroxybutyrate) blends (PCL/PHB at 50 wt%) were obtained by electrospinning and curcumin encapsulated at 1 wt% as active agent, as drug delivery systems for biomedical applications. PCL and PHB were also separately electrospinned and loaded with 1 wt% of curcumin. The processing parameters of PHB were drastically different from PCL and the blend PCL/PHB; in fact, the temperature used was 40 °C, and the distance injector–collector was 28 cm. Different conditions were used for PCL: lower temperature (i.e., 25 °C) and shorter distance injector–collector (i.e., 18 cm). The blend was processed in the same conditions of PCL. The fibers obtained with PHB showed diameters in the order of magnitude of micron (i.e., ≈ 3.45 µm), while the PCL mats is composed of fiber of nanometric dimensions (i.e., ≈ 340 nm). PCL/PHB blend allowed to obtain nanometric fibers (i.e., ≈520 nm). Same trend of results was obtained for the fibers’ porosity. The morphology, thermal, mechanical and barrier properties (sorption and diffusion) through water vapor were evaluated on all the electrospun fibers, as well as the release behavior of curcumin, and correlated to the processing parameter and the fibers’ morphologies.