The overall migration behavior and the disintegration under composting conditions of films based on plasticized poly(lactic acid)/poly(3-hydroxybutyrate) (PLA-PHB) blends were studied, with the main aim of determining the feasibility of their application as biodegradable food packaging materials. The role of composition in the disintegration process was evaluated by monitoring the changes in physical and thermal properties that originated during the degradation process. PLA and PHB were blended in two weight ratios with 15 wt% of tributyrin, using a Haake mixer and then compression molded into ~150 μm films. We found that the migration level of all of the studied blends was below check intended meaning retained in non-polar simulants, while only plasticized blends could withstand the contact with polar solvents. The disintegration of all of the materials in compost at 58 °C was completed within 42 days; the plasticized PHB underwent the fastest degradation, taking only 14 days. The presence of the TB plasticizer speeded up the degradation process. Different degradation mechanisms were identified for PLA and PHB. To evaluate the annealing effect separately from bacteria degradation, the influence of temperature on materials in the absence of a compost environment was also studied. With the increasing time of degradation in compost, both melting temperature and maximum degradation temperature progressively decreased, while the crystallinity degree increased, indicating that the samples were definitely degrading and that the amorphous regions were preferentially eroded by bacteria.