This study investigates the effects of four multifunctional chain-extending cross-linkers (CECL) on the processability, mechanical performance, and structure of polybutylene adipate terephthalate (PBAT) and polylactic acid (PLA) blends produced using film blowing technology. The newly developed reference compound (M·VERA® B5029) and the CECL modified blends are characterized with respect to the initial properties and the corresponding properties after aging at 50 °C for 1 and 2 months. The tensile strength, seal strength, and melt volume rate (MVR) are markedly changed after thermal aging, whereas the storage modulus, elongation at the break, and tear resistance remain constant. The degradation of the polymer chains and crosslinking with increased and decreased MVR, respectively, is examined thoroughly with differential scanning calorimetry (DSC), with the results indicating that the CECL-modified blends do not generally endure thermo-oxidation over time. Further, DSC measurements of 25 µm and 100 µm films reveal that film blowing pronouncedly changes the structures of the compounds. These findings are also confirmed by dynamic mechanical analysis, with the conclusion that tris(2,4-di-tert-butylphenyl)phosphite barely affects the glass transition temperature, while with the other changes in CECL are seen. Cross-linking is found for aromatic polycarbodiimide and poly(4,4-dicyclohexylmethanecarbodiimide) CECL after melting of granules and films, although overall the most synergetic effect of the CECL is shown by 1,3-phenylenebisoxazoline.