This study proposes the use of carbon nanotubes (CNTs) as reinforcement to enhance the mechanical properties of a polylactide-caprolactone copolymer (PLC) matrix. Biological interaction of PLC-CNT composites with human osteoblast cells is also investigated. Addition of 2 wt % CNT shows very uniform dispersion in the copolymer matrix, whereas 5 wt % CNT shows severe agglomeration and high porosity. PLC-2 wt % CNT composite shows an improvement in the mechanical properties with an increase in the elastic modulus by 100% and tensile strength by 160%, without any adverse effect on the ductility up to 240% elongation. An in vitro biocompatibility study on the composites shows an increase in the viability of human osteoblast cells compared to the PLC matrix, which is attributed to the combined effect of CNT content and surface roughness of the composite films.