Nanofibrous mats provide substantial delamination hindering in composite laminates, especially if the polymer (as rubbers) can directly toughen the composite resin. Here, the well-known Nylon 66 nanofibers were impregnated with Nitrile Butadiene Rubber (NBR) for producing rubber/thermoplastic membranes for hampering the delamination of epoxy Carbon Fiber Reinforced Polymers (CFRPs). The starting polyamide mats were electrospun using two different solvent systems, and their effect on the mat's thermal and mechanical properties was investigated, as well as the laminate Mode I delamination resistance via Double Cantilever Beam (DCB) tests. Plain Nylon 66 mats electrospun from formic acid/chloroform perform better than the ones obtained from a solvent system containing trifluoroacetic acid, showing up to + 64% vs + 53% in interlaminar fracture toughness (GI), respectively. The effect of NBR coating benefits both nanofiber types, significantly raising the GI. The best results are obtained when interleaving medium-thickness and lightweight mats (20 µm, 9–10 g/m2) with 70–80 wt% of loaded rubber, achieving up to + 180% in GI. The work demonstrates the ability of NBR at improving the delamination hindering of common polyamide nonwovens, paving the way to the use of NBR-coated Nylon 66 nanofibers as effective interleaves for GI enhancement and overall composite safety improvement.