Novel biodegradable biomaterials were investigated for potential application in bone tissue engineering. The biomaterials were prepared by blending poly(ε-caprolactone) and thermoplastic zein, a corn protein, with or without the incorporation of hydroxyapatite particles. The biomaterials were characterized in vitro to assess the degradation in phosphate buffer saline for 56 days by monitoring weight change, morphology, wettability, and tensile properties. The interaction between the biomaterials and MG63 was evaluated by proliferation, morphological characterization, and osteogenic differentiation assays up to 28 days in in vitro cultures. The incorporation of thermoplastic zein within poly(ε-caprolactone) enhanced the hydrophilicity and degradability, while minor effects were observed after the inclusion of the hydroxyapatite particles. Compared to the neat poly(ε-caprolactone), the multiphase poly(ε-caprolactone)/thermoplastic zein–hydroxyapatite composite improved the osteogenic differentiation of MG63 cells and is being considered a candidate material for bone tissue engineering applications.