Biodegradable multiblock copolymers based on poly[(3-hydroxybutyrate)-co-(3-hydroxyvalerate)] (PHBV), poly(e-caprolactone) (PCL), and polyhedral oligomeric silsesquioxane (POSS) were synthesized by one-step copolymerization with 1,6-hexamethylene diisocyanate (HDI) as a coupling agent. The chemical structures, molecular weight, and polydispersity index of the PHBV/PCL/POSS multiblock copolymers were confirmed by 1H NMR, FTIR, and gel permeation chromatography (GPC). XRD analysis illustrated that PHBV and POSS blocks in multiblock copolymers with high content of PHBV and POSS could crystallize to form separate crystalline phases. DSC analysis indicated that the mutual interference of crystallization of PHBV, PCL, and POSS blocks existed. Compared with the crystallinity of PHBV-diol and original PHBV, the crystallinity of PHBV block decreased from 54.8 (original PHBV) and 49.5 (PHBV-diol) to 25.5%. TG measurement revealed that thermal degradation of the multiblock copolymers proceeded by a four-step degradation process and the thermal degradation behavior of PHBV block was similar to that of the original PHBV. The melt processing window of multiblock copolymers was much wider than that of the original PHBV. The results of tensile testing showed that the tensile strength at break of the fibrous membranes of multiblock copolymers increased by 37.5% from 0.8 to 1.1 MPa and the elongation at break reached 307.8%.