Increasing studies have shown bugs in multi-language software as a critical loophole in modern software quality assurance, especially those induced by language interactions (i.e., multilingual bugs). Yet existing tool support for bug detection/localization remains largely limited to single-language software, despite the long-standing prevalence of multi-language systems in various real-world software domains. Extant static/dynamic analysis and deep learning (DL) based approaches all face major challenges in addressing multilingual bugs. In this paper, we present xLoc, a DL-based technique/tool for detecting and localizing multilingual bugs. Motivated by results of our bug-characteristics study on top locations of multilingual bugs, xLoc first learns the general knowledge relevant to differentiating various multilingual control-flow structures. This is achieved by pre-training a Transformer model with customized position encoding against novel objectives. Then, xLoc learns task-specific knowledge for the task of multilingual bug detection/localization, through another new position encoding scheme (based on cross-language API vicinity) that allows for the model to attend particularly to control-flow constructs that bear most multilingual bugs during fine-tuning. We have implemented xLoc for Python-C software and curated a dataset of 3,770 buggy and 15,884 non-buggy Python-C samples, which enabled our extensive evaluation of xLoc against two state-of-the-art baselines: fine-tuned CodeT5 and zero-shot ChatGPT. Our results show that xLoc achieved 94.98% F1 and 87.24%@Top-1 accuracy, which are significantly (up to 162.88% and 511.75%) higher than the baselines. Ablation studies further confirmed significant contributions of each of the novel design elements in xLoc. With respective bug-location characteristics and labeled bug datasets for fine-tuning, our design may be applied to other language combinations beyond Python-C.