Novel ternary nanocomposites based on a thermoset (TS) system composed of triglycidyl p-aminophenol (TGAP) epoxy resin and 4,4'-diaminodiphenylsulfone (DDS) curing agent incorporating 5 wt% of a semicrystalline thermoplastic (TP), an ethylene/1-octene copolymer, and 0.5 or 1.0 wt% multi-walled carbon nanotubes (MWCNTs) have been prepared via physical blending and curing. The influence of the TP and the MWCNTs on the curing process, morphology, thermal and mechanical properties of the hybrid nanocomposites has been analyzed. Different morphologies evolved depending on the CNT content: the material with 0.5 wt% MWCNTs showed a matrix-dispersed droplet-like morphology with well-dispersed nanofiller that selectively located at the TS/TP interphase, while that with 1.0 wt% MWCNTs exhibited coarse dendritic TP areas containing agglomerated MWCNTs. Although the cure reaction was accelerated in its early stage by the nanofillers, curing occurred at a lower rate since these obstructed chain crosslinking. The nanocomposite with lower nanotube content displayed two crystallization peaks at lower temperature than that of pure TP, while a single peak appearing at similar temperature to that of TP was observed for the blend with higher nanotube loading. The highest thermal stability was found for TS/TP (5.0 wt%)/MWCNTs (0.5 wt%), due to a synergistic barrier effect of both TP and the nanofiller. Moreover, this nanocomposite displayed the best mechanical properties, with an optimal combination of stiffness, strength and toughness. However, poorer performance was found for TS/TP (5.0 wt%)/MWCNTs (1.0 wt%) due to the less effective reinforcement of the agglomerated nanotubes and the coalescence of the TP particles into large areas. Therefore, finely tuned morphologies and properties can be obtained by adjusting the nanotube content in the TS/TP blends, leading to high-performance hybrid nanocomposites suitable for structural and high-temperature applications.