This study investigates the osteogenic differentiation of umbilical-cord-derived human mesenchymal stromal cells (hUC-MSCs) on biphasic calcium phosphate (BCP) scaffolds derived from cuttlefish bone doped with metal ions and coated with polymers. First, the in vitro cytocompatibility of the undoped and ion-doped (Sr2+, Mg2+ and/or Zn2+) BCP scaffolds was evaluated for 72 h using Live/Dead staining and viability assays. From these tests, the most promising composition was found to be the BCP scaffold doped with strontium (Sr2+), magnesium (Mg2+) and zinc (Zn2+) (BCP-6Sr2Mg2Zn). Then, samples from the BCP-6Sr2Mg2Zn were coated with poly(ԑ-caprolactone) (PCL) or poly(ester urea) (PEU). The results showed that hUC-MSCs can differentiate into osteoblasts, and hUC-MSCs seeded on the PEU-coated scaffolds proliferated well, adhered to the scaffold surfaces, and enhanced their differentiation capabilities without negative effects on cell proliferation under in vitro conditions. Overall, these results suggest that PEU-coated scaffolds are an alternative to PCL for use in bone regeneration, providing a suitable environment to maximally induce osteogenesis.