In this article, we demonstrate fabricating polypropylene (PP)/multiwalled carbon nanotube (MWCNT) nanocomposite fiber veils and use them as interleaves in single-polymer composites (SPCs) to enhance their thermal and mechanical properties. With this regard, we produced a hierarchical composite structure made of a film, a woven fabric and a fine fiber mat made of the same polymer. The nanocomposite fiber mats were generated by melt-blowing.Results implied that incorporating MWCNT increased the viscosity of the melt blowing grade PP resin. Increasing MWCNT content increased the average fiber diameter and pore size by 2.1-fold and 2.5-fold, respectively. Incorporating MWCNT enhanced the melt-blown (MB) fiber mat's specific strength by 78% and improved the thermal stability. We generated multiscale SPCs by film-stacking, for which we applied a PP film as a matrix, a PP-woven fabric as the primary reinforcement, and the MB fiber mats as interleaves. The SPC's tensile modulus was improved by 37% by the interleaving. Our findings implied that the MWCNT-doped PP fiber mat interleaving provides a robust interfacial adhesion and higher damage tolerance under tensile load. Master curves were constructed from dynamic mechanical analysis frequency sweep tests based on the time-temperature superposition principle. The storage modulus increased by 33%, while the tanδ decreased around 10% with PP/MWCNT fiber mat interleaving. The developed multiscale SPC with MWCNT fiber mat interleaving veils may be easily integrated into engineering composite applications due to its cost-efficiency, fair recycling, straightforward processing, enhanced stiffness, and interfacial adhesion.