The development of an engineered non-contact multicellular coculture model that can mimic the in vivo cell microenvironment of human tissues remains challenging. In this study, we successfully fabricated a cell-container-like scaffold composed of β-tricalcium phosphate/hydroxyapatite (β-TCP/HA) bioceramic that contains four different pore structures, including triangles, squares, parallelograms, and rectangles, by means of three-dimensional (3D) printing technology. These scaffolds can be used to simultaneously culture four types of cells in a non-contact way. An engineered 3D coculture model composed of human bone-marrow-derived mesenchymal stem cells (HBMSCs), human umbilical vein endothelial cells (HUVECs), human umbilical vein smooth muscle cells (HUVSMCs), and human dermal fibroblasts (HDFs) with a spatially controlled distribution was constructed to investigate the individual or synergistic effects of these cells in osteogenesis and angiogenesis. The results showed that three or four kinds of cells cocultured in 3D cell containers exhibited a higher cell proliferation rate in comparison with that of a single cell type. Detailed studies into the cell–cell interactions between HBMSCs and HUVECs revealed that the 3D cell containers with four separate spatial structures enhanced the angiogenesis and osteogenesis of cells by amplifying the paracrine effect of the cocultured cells. Furthermore, the establishment of multicellular non-contact systems including three types of cells and four types of cells, respectively, cocultured in 3D cell containers demonstrated obvious advantages in enhancing osteogenic and angiogenic differentiation in comparison with monoculture modes and two-cell coculture modes. This study offers a new direction for developing a scaffold-based multicellular non-contact coculture system for tissue regeneration.