Value of the Data •The data provide information about total, ribosome-free, monosomal and polysomal RNA from hASCs during early adipogenesis and osteogenesis. •This dataset may be explored to understand the mechanisms involved in gene expression regulation involved in the balance between stemness and differentiation. •The information here provided may be used for future studies on triggering hASC differentiation processes. •The dataset can be used for direct comparison between adipogenesis and osteogenesis, or focused on the translational dynamic of individual transcripts, as well as studies about non-coding RNA expression and their interaction with the translational machinery.