The inherent shortcomings of fully biodegradable poly(butylene adipate-co-terephthalate) (PBAT) copolyesters including low strength, modulus, and melt viscoelasticity were addressed by melt blending of PBAT with high-stiffness and biological poly(3-hydroxybutyrate-co-4-hydroxybutyrate) (P34HB). An epoxy-based chain extender was used to increase interfacial adhesion of partially miscible PBAT/P34HB (70wt/30wt) blends. The addition of chain extender refined phase-separated morphology of blends from SEM and decreased the degree of crystallinity by DSC. Compared with neat PBAT, PBAT/P34HB blends with chain extender showed much higher melt viscosity and elasticity, as indicated by rheological properties analyses. Compared with the PBAT/P34HB blend without chain extender, the breaking strength and elongation at break of PBAT/P34HB blend with incorporation of 1 wt% ADR were increased by 91.8% and 58.7%, respectively. It could be concluded that the combination of blending and chain-extension reaction simultaneously improved the strength, elongation at break, and melt viscoelasticity, which contributed to the suitability of biodegradable polymer blends for a wider range of end-use applications.