Chromatin states must be maintained during cell proliferation to uphold cellular identity and genome integrity. Inheritance of histone modifications is central in this process. However, the histone modification landscape is challenged by incorporation of new unmodified histones during each cell cycle, and the principles governing heritability remain unclear. We take a quantitative computational modeling approach to describe propagation of histone H3K27 and H3K36 methylation states. We measure combinatorial H3K27 and H3K36 methylation patterns by quantitative mass spectrometry on subsequent generations of histones. Using model comparison, we reject active global demethylation and invoke the existence of domains defined by distinct methylation endpoints. We find that H3K27me3 on pre-existing histones stimulates the rate of de novo H3K27me3 establishment, supporting a read-write mechanism in timely chromatin restoration. Finally, we provide a detailed quantitative picture of the mutual antagonism between H3K27 and H3K36 methylation and propose that it stabilizes epigenetic states across cell division.