The introduction of nanostructured interlayers is one of the most promising strategies for interlaminar reinforcement in structural composites. In this work, we study the failure mechanism and interlayer microstructure of aerospace-grade structural composites reinforced with thin veils of carbon nanotube produced using an industrialised spinning process. Samples of unidirectional carbon fibre/epoxy matrix composites interleaved with different composition CNT veils were prepared using hot press method and tested for interlaminar fracture toughness (IFT), measured in Mode-I (opening) and Mode-II (in-plane shear), and for interlaminar shear strength (ILSS), evaluated by the short beam shear (SBS) test. The crack propagation mode could be directly determined through fractography analysis by electron microscopy and resin/CNT spatial discrimination by Raman spectroscopy, showing a clear correlation between interlaminar reinforcement and the balance between cohesive/adhesive failure mode at the interlayer region. Composites with full resin infiltration of the CNT veils give a large increase of Mode II IFT (88%) to 1500 J/m2 and a slight enhancement of apparent interlaminar shear strength (6.5%), but a decrease of Mode I IFT (-21%). The results help establish the role of interlayer infiltration, interlaminar crossings and formation of a carbon fibre bridgings, for interlaminar reinforcement with interleaves.