While the brittle polylactide (PLA) has a high durability among bioplastics, poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (PHBH) with certain ductility exhibits facile compostability. The addition of polybutylene adipate terephthalate (PBAT) may also be used to improve the ductility and toughness of brittle bioplastics. Binary and ternary blends of PLA/PBAT/PHBH based on either PLA or PHBH as the matrix have been manufactured using a twin-screw extruder. The melt rheological, mechanical, and morphological properties of the processed samples were examined. Binary blends of PLA/PHBH show superior strength, with the PLA75/PHBH25 blend exhibiting a tensile strength of 35.2 ± 3.0 MPa, which may be attributed to miscible-like morphology. In contrast, blends of PLA with PBAT demonstrate low strength, with the PLA50/PBAT50 blend exhibits a tensile strength of 9.5 ± 2.0 MPa due to the presence of large droplets in the matrix. PBAT-containing blends exhibit lower impact strengths compared to PHBH-containing blends. For instance, a PLA75/PBAT25 blend displays an impact strength of 1.76 ± 0.1 kJ/m, whereas the PHBH75/PBAT25 blend displays an impact strength of 2.61 ± 0.3 kJ/m, which may be attributed to uniformly dispersed PBAT droplets.