The mechanical properties of the matrix and the fiber/matrix interface have a relevant influence over the mechanical properties of a composite. In this work, a glass fiber-reinforced composite is manufactured using a carbon nanotubes (CNTs) doped epoxy matrix. The influence of the CNTs on the material mechanical behavior is evaluated on the resin, on the fiber/matrix interface, and on the composite. On resin, the incorporation of CNTs increased the hardness by 6% and decreased the fracture toughness by 17%. On the fiber/matrix interface, the interfacial shear strength (IFSS) increased by 22% for the nanoengineered composite (nFRC). The influence of the CNTs on the composite behavior was evaluated by through-thickness compression, short beam flexural, and intraply fracture tests. The compressive strength increased by 6% for the nFRC, attributed to the rise of the matrix hardness and the fiber/matrix IFSS. In contrast, the interlaminar shear strength (ILSS) obtained from the short beam tests was reduced by 8% for the nFRC; this is attributed to the detriment of the matrix fracture toughness. The intraply fracture test showed no significant influence of the CNTs on the fracture energy; however, the failure mode changed from brittle to ductile in the presence of the CNTs.