Graphene, graphene-based nanomaterials (GBNs), and carbon nanotubes (CNTs) are being investigated as potential substrates for the growth of neural cells. However, in most in vitro studies, the cells were seeded on these materials coated with various proteins implying that the observed effects on the cells could not solely be attributed to the GBN and CNT properties. Here, we studied the biocompatibility of uncoated thermally reduced graphene (TRG) and poly(vinylidene fluoride) (PVDF) membranes loaded with multi-walled CNTs (MWCNTs) using neural stem cells isolated from the adult mouse olfactory bulb (termed aOBSCs). When aOBSCs were induced to differentiate on coverslips treated with TRG or control materials (polyethyleneimine-PEI and polyornithine plus fibronectin-PLO/F) in a serum-free medium, neurons, astrocytes, and oligodendrocytes were generated in all conditions, indicating that TRG permits the multi-lineage differentiation of aOBSCs. However, the total number of cells was reduced on both PEI and TRG. In a serum-containing medium, aOBSC-derived neurons and oligodendrocytes grown on TRG were more numerous than in controls; the neurons developed synaptic boutons and oligodendrocytes were more branched. In contrast, neurons growing on PVDF membranes had reduced neurite branching, and on MWCNTs-loaded membranes oligodendrocytes were lower in numbers than in controls. Overall, these findings indicate that uncoated TRG may be biocompatible with the generation, differentiation, and maturation of aOBSC-derived neurons and glial cells, implying a potential use for TRG to study functional neuronal networks.