Ancient Buddhist literature features frequent, yet often unannotated, textual parallels spread across diverse languages: Sanskrit, Pāli, Buddhist Chinese, Tibetan, and more. The scale of this material makes manual examination prohibitive. We present the MITRA framework, which consists of a novel pipeline for multilingual parallel passage mining, MITRA-parallel, a large-scale corpus of 1.74 million parallel sentence pairs between Sanskrit, Chinese, and Tibetan, and the development of the domain-specific pretrained language model Gemma 2 MITRA. We present Gemma 2 MITRA-MT, a version of this base model fine-tuned on machine translation tasks, reaching state-of-the-art performance for machine translation of these languages into English and outperforming even much larger open-source models. We also present Gemma 2 MITRA-E, a semantic embedding model that shows state-of-the-art performance on a novel, detailed semantic embedding benchmark. We make the parallel dataset, model weights, and semantic similarity benchmark openly available to aid both NLP research and philological studies in Buddhist and classical Asian literature.