In the present study, a new poly(3-hydroxybutyrate-co-3-hydroxyvalerate-co-3-hydroxyhexanoate) [P(3HB-co-3HV-co-3HHx)] terpolyester with approximately 68 mol% of 3-hydroxybutyrate (3HB), 17 mol% of 3-hydroxyvalerate (3HV), and 15 mol% of 3-hydroxyhexanoate (3HHx) was obtained via the mixed microbial culture (MMC) technology using fruit pulps as feedstock, a processing by-product of the juice industry. After extraction and purification performed in a single step, the P(3HB-co-3HV-co-3HHx) powder was melt-mixed, for the first time, in contents of 10, 25, and 50 wt% with commercial poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV). Thereafter, the resultant doughs were thermo-compressed to obtain highly miscible films with good optical properties, which can be of interest in rigid and semirigid organic recyclable food packaging applications. The results showed that the developed blends exhibited a progressively lower melting enthalpy with increasing the incorporation of P(3HB-co-3HV-co-3HHx), but retained the PHB crystalline morphology, albeit with an inferred lower crystalline density. Moreover, all the melt-mixed blends were thermally stable up to nearly 240 °C. As the content of terpolymer increased in the blends, the mechanical response of their films showed a brittle-to-ductile transition. On the other hand, the permeabilities to water vapor, oxygen, and, more notably, limonene were seen to increase. On the overall, this study demonstrates the value of using industrial biowaste derived P(3HB-co-3HV-co-3HHx) terpolyesters as potentially cost-effective and sustainable plasticizing additives to balance the physical properties of organic recyclable polyhydroxyalkanoate (PHA)-based food packaging materials.