Epoxy composites are widely used in primary aerospace structures, where high impact damage properties are necessary. However, challenges appear when multiple functionalities, including electrical and thermal conductivity, are needed in parallel with increased mechanical properties. The current study aims at the assessment of a critical concentration of multiwalled carbon nanotubes (MWCNTs), incorporated in epoxy resin, which will indicate a threshold for optimal electrical, thermal and mechanical properties. For the evaluation of this optimal concentration, electrical conductivity, thermal stability and nanomechanical properties (Young modulus and nanohardness) have been assessed, for epoxy nanocomposites with 0 to 15 parts per hundred resin per weight (phr) MWCNTs. Percolation theory was applied to study the electrical conductivity for different contents of MWCNTs in the epoxy nanocomposite system. Thermogravimetric analysis was employed for the assessment of the epoxy composites’ thermal properties. Nanohardness and elastic modulus were measured, and the hardness versus modulus index was calculated. Emphasis was given to the dispersion of MWCNTs in the epoxy matrix, which was assessed by both microscopy techniques and X-ray micro–computed tomography. A correlation between the optimum dispersion and MWCNTs content in terms of electrical conductivity, thermal stability, and nanomechanical properties revealed a threshold concentration at 3 phr, allowing the manufacturing of aerospace structures with multifunctional properties.