MOTIVATION: Generative models have demonstrated considerable promise in de novo protein design. Traditional approaches typically focus on either sequence or structure in isolation, limiting the capacity to explore the intricate sequence-structure landscape and achieve optimal designs. However, joint protein sequence and structure co-design remains a largely underexplored challenge. RESULTS: We present CoFlow, a discrete model for protein co-design from scratch or given constraints. CoFlow employs a joint discrete flow and integrates a multi-modal protein masked language model to facilitate co-design in the discrete space. Comprehensive experiments demonstrate that CoFlow outperforms previous design methods across multiple evaluation metrics. Notably, CoFlow achieves a consistency approximately eight times higher than that of ESM3 in unconditional generation. Moreover, CoFlow exhibits competitive performance in conditional generation tasks, including motif-scaffolding, protein folding, and inverse folding. AVAILABILITY AND IMPLEMENTATION: The source code of CoFlow, including data preprocessing and model, is available at https://github.com/LtECoD/CoFlow and https://zenodo.org/records/14842367. (DOI: 10.5281/zenodo.14842367).