The influence of two types of a styrene-ethylene/butylene-styrene (SEBS) triblock copolymer, one as received and the other functionalized with maleic anhydride, on model interfaces of high-density polyethylene (HDPE) and isotactic polypropylene (iPP) was investigated. Using a special preparation technique, it was possible to prevent gross interdiffusion at the interface and to attribute the problem to an adhesion-dominated phenomenon. The weak mechanical strength of the unmodified interfaces, iPP/iPP and HDPE/HDPE, was greatly improved by the triblock copolymer as was shown by the results of a T-peel test. The morphologies of the peeled surfaces of the modified and unmodified interfaces were analysed with light microscopy. The morphology of both model interface systems show differences, thus revealing different processes at the interfaces and thus different interactions of SEBS with iPP and HDPE and a different influence of the functionalization. The best results were achieved using the functionalized SEBS; the influence of functionalization was greater in the HDPE system. The results are in good agreement with a model proposed by the present authors elsewhere for the concentration-dependent role of SEBS in binary iPP/SEBS and ternary iPP/PE/SEBS blends.