Marrying topic models and language models expose language understanding to a broader source of document-level context beyond sentences via topics. While introducing topical semantics in language models, existing approaches incorporate latent document topic proportions and ignore topical discourse in sentences of the document. This work extends the line of research by additionally introducing an explainable topic representation in language understanding, obtained from a set of key terms correspondingly for each latent topic of the proportion. Moreover, we retain sentence-topic associations along with document-topic association by modeling topical discourse for every sentence in the document. We present a novel neural composite language model that exploits both the latent and explainable topics along with topical discourse at sentence-level in a joint learning framework of topic and language models. Experiments over a range of tasks such as language modeling, word sense disambiguation, document classification, retrieval and text generation demonstrate ability of the proposed model in improving language understanding.