Task-oriented dialogue understanding remains underexplored for Bangla, particularly in multilingual settings involving English and romanized Bangla (Banglish). We introduce BanglaTOD, a parallel tri-lingual benchmark comprising 209 multi-turn dialogues across nine Bangladesh-specific service domains and 64 intents. Each conversational turn is aligned across Bangla, English, and Banglish, yielding 4,689 language-specific turn records annotated with intents, token-level slots, state updates, and accumulated dialogue states. We establish context-aware baselines for joint intent classification and slot filling using mBERT, BERT-base-uncased, and BanglaBERT. Cross-language analysis reveals substantial performance differences across models and linguistic representations, while removing dialogue history reduces intent accuracy by 19.0--25.7 percentage points. BanglaTOD provides a foundation for multilingual dialogue understanding and future dialogue state tracking research in Bangladesh-specific conversational applications. The dataset is publicly available at \href{https://huggingface.co/datasets/afri7here/BanglaTOD}{Hugging Face}.

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