Carbon nanotubes (CNTs) demonstrate extraordinary properties and show great promise in enhancing out-of-plane properties of traditional polymer composites and enabling functionality, but current manufacturing challenges hinder the realization of their potential. This paper presents a method to fabricate multifunctional multiscale composites through an effective infiltration-based vacuum-assisted resin transfer moulding (VARTM) process. Multi-walled carbon nanotubes (MWNTs) were infused through and between glass-fibre tows along the through-thickness direction. Both pristine and functionalized MWNTs were used in fabricating multiscale glass-fibre-reinforced epoxy composites. It was demonstrated that the mechanical properties of multiscale composites were remarkably enhanced, especially in the functionalized MWNT multiscale composites. With only 1 wt% loading of functionalized MWNTs, tensile strength was increased by 14% and Young's modulus by 20%, in comparison with conventional fibre-reinforced composites. Moreover, the shear strength and short-beam modulus were increased by 5% and 8%, respectively, indicating the improved inter-laminar properties. The strain-stress tests also suggested noticeable enhancement in toughness. Scanning electron microscopy (SEM) characterization confirmed an enhanced interfacial bonding when functionalized MWNTs were integrated into epoxy/glass-fibre composites. The coefficient thermal expansion (CTE) of functionalized nanocomposites indicated a reduction of 25.2% compared with epoxy/glass-fibre composites. The desired improvement of electrical conductivities was also achieved. The multiscale composites indicated a way to leverage the benefits of CNTs and opened up new opportunities for high-performance multifunctional multiscale composites.