DNA-RNA hybrids arise in all cell types, and are removed by multiple enzymes, including the trimeric ribonuclease, RNase H2. Mutations in human RNase H2 result in Aicardi-Goutières syndrome (AGS), an inflammatory brain disorder notable for being a Mendelian mimic of congenital viral infection. Previous studies have shown that several AGS-associated mutations of the RNase H2B subunit do not affect trimer stability or catalytic activity and are clustered on the surface of the complex, leading us to speculate that these mutations might impair important interactions of RNase H2 with so far unidentified proteins. In this study, we show that AGS mutations in this cluster impair the interaction of RNase H2 with several members of the CoREST chromatin-silencing complex that include the histone deacetylase HDAC2 and the demethylase KDM1A, the transcriptional regulators RCOR1 and GTFII-I as well as ZMYM3, an MYM-type zinc finger protein. We also show that the interaction is mediated by the zinc finger protein ZMYM3, suggesting that ZMYM3 acts as a novel type of scaffold protein coordinating interactions between deacetylase, demethylase and RNase H type enzymes, raising the question of whether coordination between histone modifications and the degradation of RNA-DNA hybrids may be required to prevent inflammation in humans.