In this research a biodegradable blend of poly(ɛ-caprolactone) (PCL) and poly(lactic acid) (PLA) is proposed as a new material for the production of a relief printing plate used for special applications on packaging materials, i.e., the embossing process. Coconut fibers (CFs) were added as a natural filler to PCL/PLA blends to improve the functional properties of the prepared blends. Thermal, mechanical and surface analyses were performed on the unaged and artificially aged blends. The results showed that CF has been proven to optimize the hardness of the blend, which is crucial for the production of relief plate for embossing applications. The lowest hardness was measured on neat PCL (53.30° Sh D) and the highest value on PCL/PLA/CF 70/30/3.0 blend (60.13° Sh D). Stronger interfacial interactions were present at the PLA/CF interface because the interfacial free energy is closer to zero and the work of adhesion and spreading coefficient are higher than for the PCL/CF interface. The results of thermal analysis of unaged and aged blends showed that ageing for 3 weeks resulted in significantly lower thermal stability, especially for neat PCL and PCL/PLA 80/20 blends. Blends with a higher content of PLA and CF showed a slightly increased ageing resistance, which is attributed to the increased crystallinity of PLA after ageing due to the addition of CF showed in the DSC diagrams.