In this study, the optimized formulations of polycaprolactone (PCL) combined with poly(lactic-co-glycolic acid) (PLGA), gelatin (GEL), and biphasic calcium phosphate (BCP) were analyzed in terms of cytocompatibility with bone-related cells, hemocompatibility, and in vivo bone-regenerating capacity to determine their potentials for bone tissue regeneration. Fiber morphology of PCL/GEL and PCL/BCP electrospun mats considerably differs from that of the PCL membrane. Based on the contact angle analyses, the addition of GEL and PLGA was shown to reduce the hydrophobicity of these membranes. The assessment of in vitro cytocompatibility using MC3T3-E1 cells indicated that all of the membranes were suitable for pre-osteoblast proliferation and adhesion, with PCL/BCP having a significantly higher reading after seven days of incubation. The results of the in vitro hemocompatibility of the different fibrous scaffolds suggest that coagulation and platelet adhesion were higher for hydrophobic membranes (PCL and PCL/PLGA), while hemolysis can be associated with fiber morphology. The potential of the membranes for bone regeneration was determined by analyzing the microCT data and tissue sections of samples implanted in 5 mm sized defects (one and two months). Although all of the membranes were suitable for pre-osteoblast proliferation, in vivo bone regeneration after two months was found to be significantly higher in PCL/BCP (p < 0.001).