Addressing the problem of vascularization is of vital importance when engineering three-dimensional (3D) tissues. Endothelial cells are increasingly used in tissue-engineered constructs to obtain prevascularization and to enhance in vivo neovascularization. Rat bone marrow stromal cells were cultured in thermoresponsive dishes under osteogenic conditions with human umbilical vein endothelial cells (HUVECs) to obtain homotypic or heterotypic cell sheets (CSs). Cells were retrieved as sheets from the dishes after incubation at 20 °C. Monoculture osteogenic CSs were stacked on top of homotypic or heterotypic CSs, and subcutaneously implanted in the dorsal flap of nude mice for 7 days. The implants showed mineralized tissue formation under both conditions. Transplanted osteogenic cells were found at the new tissue site, demonstrating CS bone-inductive effect. Perfused vessels, positive for human CD31, confirmed the contribution of HUVECs for the neovascularization of coculture CS constructs. Furthermore, calcium quantification and expression of osteocalcin and osterix genes were higher for the CS constructs, with HUVECs demonstrating the more robust osteogenic potential of these constructs. This work demonstrates the potential of using endothelial cells, combined with osteogenic CSs, to increase the in vivo vascularization of CS-based 3D constructs for bone tissue engineering purposes.