The composite materials of the polymeric matrix reinforced with carbon fibre have an extensive industrial application as they provide light and resistant structures. However, in many products (automobiles, aircraft, etc.), the composite materials must be joined to other components manufactured with aluminium alloys. The use of structural adhesive to bond these materials may be a good alternative if a specific design of the adhesive joint is carried out by maximising its performance and reducing its limitations. In the current work, the end-notched flexure (ENF) fracture test is used to assess the mechanical behaviour of the adhesive joint to facilitate the choice of the best adhesive and surface treatment of the adherends. However, in industrial applications of a great technical requirement (where the safety of staff or property may be at risk), the former experimental results are not enough and must be complemented with methods that can provide additional guarantee for a suitable reliability. For this purpose, a statistic analysis of the obtained experimental data has been carried out by means of the application of a Weibull distribution, in order to propose the adhesive and surface treatment that best combines the mechanical performance and high reliability. At the end, we can conclude that the epoxy adhesive with sand-blasting treatment for the aluminium and the peel ply for the carbon fibre has the greatest reliability (more than 90% for loads until 900N).