We introduce DisSim, a discourse-aware sentence splitting framework for English and German whose goal is to transform syntactically complex sentences into an intermediate representation that presents a simple and more regular structure which is easier to process for downstream semantic applications. For this purpose, we turn input sentences into a two-layered semantic hierarchy in the form of core facts and accompanying contexts, while identifying the rhetorical relations that hold between them. In that way, we preserve the coherence structure of the input and, hence, its interpretability for downstream tasks.