This work evaluated the thermal properties and biocompatibility of composites of polyhydroxyalkanoate (PHA) and hyaluronic acid (HA) (PHA/HA). Maleic anhydride (MA)-grafted polyhydroxyalkanoate (PHA-g-MA) was assessed as an alternative to PHA. The lower melt torque of the PHA-g-MA/HA composites resulted in them being more easily processed than PHA/HA. The water resistance of PHA-g-MA/HA was higher than that of PHA/HA. Human foreskin fibroblasts (FBs) were seeded on two series of these composites to assess cytocompatibility. Collagen and cell proliferation analyses indicated that PHA and PHA-g-MA and their composites were biocompatible with respect to FB proliferation. However, FB proliferation, collagen production, and the percentage of normal cells growing on PHA/HA composites were greater than those for PHA-g-MA/HA composites. Cell-cycle and apoptosis assays by FBs on the PHA series composite samples were not affected by DNA content related to damage; i.e., rapid apoptosis/necrosis was not observed, demonstrating the potential of PHA/HA or PHA-g-MA/HA membranes for biomedical material applications.