Document retrieval plays a crucial role in numerous question-answering systems, yet research has concentrated on the general knowledge domain and resource-rich languages like English. In contrast, it remains largely underexplored in low-resource languages and cross-lingual scenarios within specialized domain knowledge such as legal. We present a novel dataset designed for cross-lingual retrieval between Vietnamese and English, which not only covers the general domain but also extends to the legal field. Additionally, we propose auxiliary loss function and symmetrical training strategy that significantly enhance the performance of state-of-the-art models on these retrieval tasks. Our contributions offer a significant resource and methodology aimed at improving cross-lingual retrieval in both legal and general QA settings, facilitating further advancements in document retrieval research across multiple languages and a broader spectrum of specialized domains. All the resources related to our work can be accessed at huggingface.co/datasets/bkai-foundation-models/crosslingual.