Inherent weak interfaces exist in large plate and shell composites made from carbon fibre pre-pregs and in any laminar structures bonded by epoxy adhesives due to absence of Z-directional toughening. In-situ Z-directional movements of short and flexible fibres from ultra-thin un-bonded non-woven Aramid veils can potentially compensate for the inherent structural weakness. Incorporations of nano-fillers, carbon nano-tubes (CNT) and graphene can enhance the toughness of epoxy matrix, but cannot alter the interfacial structures of adhesive joints or provide effective Z-directional toughening. This study shows quasi-Z-directional fibre-bridging across carbon fibre plies can be created in-situ during composite processing from ultra-thin un-bonded non-woven Aramid veils between carbon fibre plies. CNT can also be incorporated into the un-bonded veils, and the hierarchical CNT and Aramid veil interfacial toughening is more effective as the hybrid fibre system can reinforce the epoxy matrix and alter the 3D interfacial structures between carbon fibre plies from movements of the free fibre ends. Un-bonded non-woven Aramid veils can be introduced during the pre-preging process. As a result, the common concept of interleaving will be changed, as the extra composite layup step is no longer required. The carbon fibre pre-pregs incorporated with ultra-thin non-woven veils can be used just as normal pre-pregs. Experiments on edge delamination in carbon fibre composites due to drilling and on adhesive bonding between aluminium plates are used to demonstrate the effectiveness of quasi-Z-directional toughening from un-bonded veils due to the out-of-plane movements of short flexible Aramid fibres.