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Coherence is an essential property of well-written texts, that refers to the way textual units relate to one another. In the era of generative AI, coherence assessment is essential for many NLP tasks such as summarization, long-form question-answering, and more.Current NLP approaches for modeling coherence often rely on a proxy task, specifically, sentence reordering. However, such an approach may not capture the full range of factors contributing to coherence.To remedy this, in this work we employ the formal linguistic definition by Reinhart:1980 of what makes a discourse coherent, consisting of three conditions, cohesion, consistency and relevance, and formalize these conditions as respective computational tasks, which are in turn jointly trained. We evaluate this modeling approach on two human-rated coherence benchmarks: one of automatically-generated stories and one of real-world texts.Our experiments show that jointly training on the proposed tasks leads to better performance on each task compared with task-specific models, and to better performance on assessing coherence overall.Our proposed computational framework thus paves the way for a more advanced, broad-coverage coherence assessment.