In this study, a tetrafunctional epoxy resin was loaded with 5 wt% of three different types of polyhedral oligomeric silsesquioxane (POSS) compounds, namely, DodecaPhenyl POSS (DPHPOSS), Epoxycyclohexyl POSS (ECPOSS), Glycidyl POSS (GPOSS), and 0.5 wt% of multi-walled carbon nanotubes (CNTs) in order to formulate multifunctional structural nanocomposites tailored for aeronautic and aerospace applications. This work aims to demonstrate how the skillful combination of desired properties, such as good electrical, flame-retardant, mechanical, and thermal properties, is obtainable thanks to the advantages connected with nanoscale incorporations of nanosized CNTs with POSS. The special hydrogen bonding-based intermolecular interactions between the nanofillers have proved to be strategic in imparting multifunctionality to the nanohybrids. All multifunctional formulations are characterized by a Tg centered at values close to 260 °C, fully satisfying structural requirements. Infrared spectroscopy and thermal analysis confirm the presence of a cross-linked structure characterized by a high curing degree of up to 94% and high thermal stability. Tunneling atomic force microscopy (TUNA) allows to detect the map of the electrical pathways at the nanoscale of the multifunctional samples, highlighting a good dispersion of the carbon nanotubes within the epoxy resin. The combined action of POSS with CNTs has allowed to obtain the highest values of self-healing efficiency if compared to those measured for samples containing only POSS in the absence of CNTs.