Histone H3 lysine 9 (H3K9) methylation and histone hypoacetylation are two conserved epigenetic hallmarks of heterochromatin. How H3K9 methylation and histone hypoacetylation are faithfully inherited and how these two processes are coordinately regulated during replication remain poorly understood. We previously showed that the inheritance of H3K9 methylation during DNA replication depends on the catalytic subunit of DNA Polymerase epsilon, Cdc20/Pol2, in fission yeast. Here we show that two histone-fold subunits of Pol epsilon, Daf1/Dpb3 and Dpb4, in fission yeast form a heterodimer that plays a crucial role in the inheritance of histone hypoacetylation. Our findings reveal a previously unrecognized link between histone deacetylation and H3K9 methylation, and suggest a mechanism for how two processes are coordinated during replication. Surprisingly, we found that Dpb4 associates with both positive and negative regulators of heterochromatin silencing. Particularly, we show that SWI/SNF chromatin remodeling complex subunits interact with Daf1-Dpb4 dimer and act an anti-silencing factor essential for heterochromatin disassembly. Upon solving the 1.9 Å crystal structure of the Daf1-Dpb4 complex we observed that Daf1 and Dpb4 form an H2A-H2B-like heterodimer, and gained further insight into the role of this dimer in chromatin regulation. To our knowledge, this represents the first time a crystal structure has been resolved for Dpb3-Dpb4. Together, our findings indicate that the Daf1-Dpb4 complex provides a platform for the recruitment of chromatin modifiers and remodelers during DNA replication, which in turn mediate the disassembly and re-assembly of heterochromatin and ensure the accurate perpetuation of heterochromatin marks.