Elucidation of interactions involving DNA and histone post-translational-modifications (PTMs) is essential for providing insights into complex biological functions. Reader assemblies connected by flexible linkages facilitate avidity and increase affinity; however, little is known about the contribution to the recognition process of multiple PTMs because of rigidity in the absence of conformational flexibility. Here, we resolve the crystal structure of the triple reader module (PHD-BRD-PWWP) of ZMYND8, which forms a stable unit capable of simultaneously recognizing multiple histone PTMs while presenting a charged platform for association with DNA. Single domain disruptions destroy the functional network of interactions initiated by ZMYND8, impairing recruitment to sites of DNA damage. Our data establish a proof of principle that rigidity can be compensated by concomitant DNA and histone PTM interactions, maintaining multivalent engagement of transient chromatin states. Thus, our findings demonstrate an important role for rigid multivalent reader modules in nucleosome binding and chromatin function.