Fused filament fabrication (FFF) has been extensively studied for conventional polymers, but there are few studies that address the processing challenges for biobased, biodegradable polymers such as poly(lactic acid) (PLA) and poly(hydroxy alkenoates) (PHA) in FFF processes. This study has investigated the elongational and shear rheological properties and thermophysical characteristics of PLA/PHA hybrid materials to determine the effects of processing conditions, including nozzle temperatures, bed temperatures, and speeds, on the quality of the PLA/PHA printed products, e.g., adhesion strength and tensile properties. Our findings showed that adding PHA to the composition of the PLA/PHA hybrid material leads to a reduction in shear and extensional viscosities, causing a rise in elongation at break and adhesion strength while showing comparable tensile strength with the PLA samples. In addition to the presence of PHA in the combination of the hybrid materials, processing conditions, including nozzle temperature, bed temperature, and print speed, were found to be effective on the adhesion strength and tensile characteristics of the printed products. Our results suggested that among processing parameters, nozzle temperature has the most significant effect on adhesion strength and tensile characteristics. Samples printed at the nozzle temperature of 215 °C showed an order of magnitude higher adhesion strength and up to 34% enhancement in elongation at break compared to the printed samples at 185 °C. This study sheds light on the significance of the material and processing parameters in obtaining quality products from biobased, biodegradable polymers.