In this work biocomposites based on plasticized poly(lactic acid) (PLA)–poly(butylene succinate-co-adipate) (PBSA) matrix containing wheat bran fiber (a low value by-product of food industry) were investigated. The effect of the bran addition on the mechanical properties is strictly correlated to the fiber-matrix adhesion and several analytical models, based on static and dynamic tests, were applied in order to estimate the interfacial shear strength of the biocomposites. Finally, the essential work of fracture approach was carried out to investigate the effect of the bran addition on composite fracture toughness.