With the widespread and increased consumption of online news, there is a rising need for automated analysis of news text. Topic models have proven to be useful tools for unsupervised discovery of topics from large amounts of text, including news media texts. Topics produced by a topic model are often represented as probability-weighted word lists, and it is expected that these bear correspondence to semantic topics-semantic concepts representable by a topic model. However, because the quality of topics varies and not all topics correspond to semantic topics in practice, much research effort has been devoted to automated evaluation of topic models. One class of popular and effective methods focuses on topic coherence as a measure of a topic's semantic interpretability and its correspondence to a semantic topic. Existing topic coherence methods calculate the coherence score based on the semantic similarity of topic-related words. However, news media texts revolve around specific news stories, giving rise to many contingent and transient topics for which topic-related words tend to be semantically unrelated. Consequently, the coherence of many news media topics is not amenable to detection via state-of-art word-based coherence measures. In this paper, we propose a novel class of topic coherence methods that estimate topic coherence based on topic documents rather than topic words. We evaluate the proposed methods on two datasets containing topics manually labeled for document-based coherence, derived from US and Croatian news text corpora. Our best-performing document-based coherence measure achieves an AUC score above 0.8, substantially outperforming a strong baseline method and state-of-art word-based coherence methods. We also demonstrate that there may be benefit in combining word-and document-based coherence measures. Lastly, we demonstrate the usefulness of document-based coherence measures for automated topic discovery from news media texts.