The poly(butylene adipate-co-terephthalate) (PBAT)/thermoplastic starch (TPS) film stands out owing to its acceptable price, low impact on the environment, and excellent mechanical properties. The main objective of this study was to improve the antioxidant properties of the PBAT/TPS film by incorporation of quercetin (Q) through the extrusion blow process. Another specific objective was to incorporate the organically modified montmorillonite (OMMT) to prolong the release of Q and improve the poor barrier properties of the PBAT/TPS/Q film. The films were analyzed in terms of their morphology, mechanical properties, gas and water barrier properties, and antioxidant and anti-UV properties. Optimization of the OMMT content resulted in a fiber-like, co-continuous morphology of the PBAT/TPS/Q film. The incorporation of quercetin enhanced the antioxidant and anti-UV properties of the PBAT/TPS film, while OMMT improved the mechanical properties, ultraviolet barriers, and gas and water barrier properties. The results show that the films incorporating Q and OMMT provided the oxygen and water barrier by up to 94 and 54%, respectively. Also, the amount of polymer required for 50% 2,2-diphenyl-1-picrylhydrazyl (DPPH) inhibition is as low as 0.03 g, and the UV transmission rate was reduced by about 50%. Moreover, PBAT/TPS/Q/OMMT films successfully delayed the decay of the banana and blueberry due to their excellent antioxidant properties and suitable water vapor permeability.