In the present work, a specific three-point bending test is applied to evaluate how the roughness can impact the bond strength (adherence) and the mechanism of interfacial failure initiation. The study is conducted using an aluminum alloy 2024-T3 as substrate and the DGEBA (polyepoxide bisphenol A diglycidyl ether) /DETA (diethylenetriamine) as adhesive, considering different abrasive surface treatments. An optimal roughness is reached to maximize the critical force during failure initiation; besides, the roughness impacted the failure propagation mechanism and the failure initiation area for each abrasive treatment. A power-law regression is considered to correlate the critical force and the failure initiation area, considering different average roughness. Local assessment using a mechanical profilometer and Scanning Electron Microscope (SEM) with Focused Ion Beam (FIB) are applied to measure the residual adhesive thickness at failure initiation and failure propagation zones as well as the initiation-to-propagation transitions. It is constated that the residual adhesive thickness is dependent on the average roughness of the substrate. Finally, Weibull’s analysis is undertaken to demonstrate that the mechanism of failure initiation for all substrate groups is essentially the same, although the failure propagation mechanism can be different.