The focus of this paper was to gain a true understanding of the impact of a multifunctional epoxide (JoncrylA (R);ADR-4368) on the interfacial properties of biopolymer blends based on poly(lactic acid) (PLA) and poly(butylene adipate-co-terephthalate) (PBAT). The effect of Joncryl on the shear rheological, morphological, and interfacial properties of the blends was systematically investigated. For the deformed drop retraction experiments, different sandwich model systems (droplet/matrix), representing various scenarios of compatibilization, were prepared, aiming to probe the role of the epoxy-functionalized chains on the interface. The decrease of the interfacial tension in the modified/compatibilized PLA_PBAT and the formation of the PLA-Joncryl-PBAT copolymer were highlighted. A new relaxation peak relative to this copolymer was detected by the relaxation spectrum. Transient start-up shear and nonlinear stress relaxation experiments were carried out and confirmed the obtained results. In addition, the interface contribution was demonstrated using the Lee and Park model. The relaxation time increased with the amount of added Joncryl. Hence, the coexistence of chain extension/branching chains coupled to the PLA-Joncryl-PBAT copolymer formation had to be taken into account to explain the improved mechanical properties.