Mimicking the complex organization of the extracellular matrix (ECM), especially its structure and dimensionality, is necessary to produce living tissues from stem cells. In compliance with a previously established role of nanofiber organization for the osteogenic differentiation of stem cells, here we used hybrid fibrinogen/poly(l‐lactide‐ε‐caprolactone) (FBG/PLCL) nanofibers arranged in aligned and honeycomb configurations, to recapitulate the highly oriented ECM of the cortical bone and the sponge‐like (i.e., honeycomb) environment of the cancellous one, respectively. Using special bilayered constructs, we demonstrate that the dimensionality (i.e., 2D vs. 3D) of the nanofibers as well as their architecture (i.e., honeycomb vs. aligned) affects differently the overall morphology and the expression of multiple osteogenic genes of human adipose‐derived mesenchymal stem cells (ADMSCs). The cells had elongated shape with markedly increased cell mobility when seeded on aligned nanofibers. Conversely, on honeycomb‐shaped nanofibers, ADMSCs initially concentrated inside the honeycomb curvatures adopting rounded morphology, but late, they formed network‐like structures overlaying the honeycomb curvatures. By employing quantitative polymerase chain reaction (qPCR), we further show that a 3D environment generally supports the multiple osteogenic response of ADMSCs, but honeycomb and aligned architectures promote rather different differentiation pathways.