The failure of bonded composite materials is accompanied by specific failure modes. These are specifically Mode I, Mode II, Mode III, and their combination (so-called mixed mode). These modes depend on the direction and type of loading. The mechanical properties describing the damage initiation and the damage evolution are unique according to the type of adhesive and present mode of failure. However, a few research studies have focused on an adhesive thicknesses greater than 0.2 mm. The main objective of this research is to investigate the mechanical properties of a bonded joint with large adhesive thickness loaded according to Modes I and II. The observed failure parameters, the cohesive and damage parameters, are identified by minimizing the difference between the force-displacement diagram obtained from the experimental data for both Mode I and Mode II. The finite element model is confronted with these parameters and is evaluated based on their agreement. Compared to other studies with a small adhesive layer thickness, the values of failure parameters are lower. The results show that the adhesive thickness has an influence on the values of cohesive and damage parameters and that these parameter values decrease significantly compared to a small adhesive thickness. The obtained parameters can be further used to predict the fracture toughness of other bonded joints loaded in any direction.