The present study deals with the development of multifunctional biphasic calcium phosphate (BCP) scaffolds coated with biopolymers—poly(ε-caprolactone) (PCL) or poly(ester urea) (PEU)—loaded with an antibiotic drug, Rifampicin (RFP). The amounts of RFP incorporated into the PCL and PEU-coated scaffolds were 0.55 ± 0.04 and 0.45 ± 0.02 wt%, respectively. The in vitro drug release profiles in phosphate buffered saline over 6 days were characterized by a burst release within the first 8h, followed by a sustained release. The Korsmeyer–Peppas model showed that RFP release was controlled by polymer-specific non-Fickian diffusion. A faster burst release (67.33 ± 1.48%) was observed for the PCL-coated samples, in comparison to that measured (47.23 ± 0.31%) for the PEU-coated samples. The growth inhibitory activity against Escherichia coli and Staphylococcus aureus was evaluated. Although the RFP-loaded scaffolds were effective in reducing bacterial growth for both strains, their effectiveness depends on the particular bacterial strain, as well as on the type of polymer coating, since it rules the drug release behavior. The low antibacterial activity demonstrated by the BCP-PEU-RFP scaffold against E. coli could be a consequence of the lower amount of RFP that is released from this scaffold, when compared with BCP-PCL-RFP. In vitro studies showed excellent cytocompatibility, adherence, and proliferation of human mesenchymal stem cells on the BCP-PEU-RFP scaffold surface. The fabricated highly porous scaffolds that could act as an antibiotic delivery system have great potential for applications in bone regeneration and tissue engineering, while preventing bacterial infections.