Poly(hydroxyalkanoates) (PHAs) are emerging as sustainable materials in packaging and medical device industries. Nevertheless, the high cost and the need to improve the mechanical properties have limited their widespread use. Blending with other bio-based polymers, such as poly(lactic acid) (PLA), has been proposed in previous studies. This study investigates the effects of temperature, azodicarbonamide (AZ, foaming agent), boron nitride (BN, filler), and multilayer film/foam coextrusion on the properties of a blend containing an amorphous PHA and PLA. The effect of twin-screw micro-compounder temperature (185 °C & 205 °C) and BN concentrations of 1, 2, 3, 5, and 10 wt% (185 °C) on the properties of the PHA/PLA blend were investigated using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and tensile testing. Design of experiments (DoE) was used to find the optimal concentrations of AZ and BN (205 °C) using JMP® software. The response surface analysis predicted an optimal design based on the target response levels (modulus, tensile strength, strain at break, and toughness). This formulation was prepared and characterized using DSC, TGA, tensile, and melt flow index (MFI) measurements. Finally, this formulation was processed via film/foam coextrusion and examined using scanning electron microscopy (SEM) and density measurements. This study demonstrated that AZ and BN can be used to manipulate the mechanical properties and crystallinity of PHA/PLA blends, while reducing the overall material cost via density reduction (20–21% for the optimal formulation). Furthermore, reducing the concentration of AZ using the I-optimal design in this study could alleviate the toxicity concerns for food packaging.