We study binary blends of asymmetric diblock copolymers (AB/AC) in selective solvents with a mesoscale model. We investigate the morphological transitions induced by the concentration of the AC block copolymer and the difference in molecular weight between the AB and AC copolymers, when segments B and C exhibit hydrogen-bonding interactions. To the best of our knowledge, this is the first work modeling mixtures of block copolymers with large differences in molecular weight. The coassembly mechanism localizes the AC molecules at the interface of A and B domains and induces the swelling of the B-rich domains. The coil size of the large molecular weight block copolymer depends only on the concentration of the short block copolymer (AC or AB), regardless of the B–C interactions. However, the B–C interactions control the morphological transitions that occur in these blends.