In this study, the tensile strength of single-lap joints (SLJs) between similar and dissimilar adherends bonded with an acrylic adhesive was evaluated experimentally and numerically. The adherend materials included polyethylene (PE), polypropylene (PP), carbon-epoxy (CFRP), and glass-polyester (GFRP) composites. The following adherend combinations were tested: PE/PE, PE/PP, PE/CFRP, PE/GFRP, PP/PP, CFRP/CFRP, and GFRP/GFRP. One of the objectives of this work was to assess the influence of the adherends stiffness on the strength of the joints since it significantly affects the peel stresses magnitude in the adhesive layer. The experimental results were also used to validate a new mixed-mode cohesive damage model developed to simulate the adhesive layer. Thus, the experimental results were compared with numerical simulations performed in ABAQUS, including a developed mixed-mode (I+II) cohesive damage model, based on the indirect use of fracture mechanics and implemented within interface finite elements. The cohesive laws present a trapezoidal shape with an increasing stress plateau, to reproduce the behaviour of the ductile adhesive used. A good agreement was found between the experimental and numerical results.