The three-dimensional (3D) marrow microenvironment plays an essential role in regulating human cord blood-derived CD34+ cells (hCB-CD34+) migration, proliferation, and differentiation. Extensive in vitro and in vivo studies have aimed to recapitulate the main components of the bone marrow (BM) niche. Nonetheless, the models are limited by a lack of heterogeneity and compound structure. Here, we fabricated coaxial extruded core-shell tubular scaffolds and extrusion-based bioprinted cell-laden mesh scaffolds to mimic the functional niche in vitro. A multicellular mesh scaffold and two different core-shell tubular scaffolds were developed with human bone marrow-derived mesenchymal stromal cells (BMSCs) in comparison with a conventional 2D coculture system. A clear cell-cell connection was established in all three bioprinted constructs. Cell distribution and morphology were observed in different systems with scanning electron microscopy (SEM). Collected hCB-CD34+ cells were characterized by various stem cell-specific and lineage-specific phenotypic parameters. The results showed that compared with hCB-CD34+ cells cocultured with BMSCs in Petri dishes, the self-renewal potential of hCB-CD34+ cells was stronger in the tubular scaffolds after 14 days. Besides, cells in these core-shell constructs tended to obtain stronger differentiation potential of lymphoid and megakaryocytes, while cells encapsulated in mesh scaffolds obtained stronger differentiation tendency into erythroid cells. Consequently, 3D bioprinting technology could partially simulate the niche of human hematopoietic stem cells. The three models have their potential in stemness maintenance and multilineage differentiation. This study can provide initial effective guidance in the directed differentiation research and related screening of drug models for hematological diseases.