Automated software debugging is a crucial task for improving the productivity of software developers. Many neural-based techniques have been proven effective for debugging-related tasks such as bug localization and program repair (or bug fixing). However, these techniques often focus only on either one of them or approach them in a stage-wise manner, ignoring the mutual benefits between them. In this work, we propose a novel unified Detect-Localize-Repair framework based on a pretrained programming language model CodeT5 to seamlessly address these tasks, named CodeT5-DLR. Specifically, we propose three objectives to adapt the generic CodeT5 for debugging: a bug detection objective to determine whether a given code snippet is buggy or not, a bug localization objective to identify the buggy lines, and a program repair objective to translate the buggy code to its fixed version. We evaluate it on each of these tasks and their combined setting on two newly collected line-level debugging datasets in Java and Python. Extensive results show that our model significantly outperforms existing baselines from both NLP and software engineering domains.