Incorporation of OH groups into PS by copolymerization with hydroxystyrene caused specific OH···OC interactions with carbonyl groups of PDLLA. PDLLA blends with PSHS16 were completely miscible across the whole composition range, showing a single glass transition. Specific interactions and phase structure were analyzed by FTIR spectroscopy and SEM. DMA around Tg using the WLF theory and Angell's dynamic fragility concept revealed that specific interactions are not acting as other topological constraints (cross‐links, crystalline lamellae, silicate layers), since they rather provide a retardation of segmental dynamics.