In this study we linked zero-dimensional polyhedral oligomeric silsesquioxane (POSS) with one-dimensional single-walled carbon nanotubes (SWCNTs) as dual-dimensional nanohybrid complexes within polybenzoxazine matrices, stabilized through noncovalent supramolecular interactions. First, we synthesized a new bifunctionalized benzoxazine (Py-Bz-T), presenting thymine (T) and pyrene (Py) units, that displayed excellent thermal properties after thermal curing, because its T moieties increased the physical cross-linking density. Second, we prepared Py-Bz-T/OBA-POSS [octuply adenine (A)-functionalized POSS] nanocomposites and investigated, using nuclear magnetic resonance and Fourier transform infrared spectroscopies, the multiple hydrogen bonding AT interactions between Py-Bz-T and OBA-POSS. Finally, we prepared Py-Bz-T/OBA-POSS/SWCNT ternary hybrid complexes dispersed in THF, stabilized through both multiple hydrogen bonding and π-π stacking interactions. Transmission electron microscopy revealed that the SWCNTs were highly dispersed and covered by the Py-Bz-T/OBA-POSS nanocomposites; these ternary hybrid complexes were stabilized through π-π interactions between Py-Bz-T/OBA-POSS and the SWCNTs, as evidenced using fluorescence spectroscopy.