Biodegradable multicomponent films based on poly(lactic acid) (PLA) and poly(3-hydroxybutyrate) (PHB) plasticized with oligomeric lactic acid (OLA), reinforced with synthetized cellulose nanocrystals (CNC) and modified by a natural additive with antimicrobial activity (carvacrol) were formulated and processed by extrusion. Morphological, mechanical, thermal, migration and barrier properties were tested to determine the effect of different components in comparison with neat poly(lactic acid). Results showed the positive effect of CNC in the five components based films, with the increase of the Young's modulus of the PLA_PHB_10Carv_15OLA, associated with an increase in the elongation at break (from 150% to 410%), by showing an OTR reduction of 67%. Disintegrability in compost conditions and enzymatic degradation were tested to evaluate the post-use of these films. All formulations disintegrated in less than 17 days, while proteinase K preferentially degraded the amorphous regions, and crystallinity degree of the nanocomposite films increased as a consequence of enzyme action.