Continual learning (CL) empowers pre-trained vision-language models to adapt effectively to novel or previously underrepresented data distributions without comprehensive retraining, enhancing their adaptability and efficiency. While vision-language models like CLIP show great promise, they struggle to maintain performance across domains in incremental learning scenarios. Existing prompt learning methods face two main limitations: 1) they primarily focus on class-incremental learning scenarios, lacking specific strategies for multi-domain task incremental learning; 2) most current approaches employ single-modal prompts, neglecting the potential benefits of cross-modal information exchange. To address these challenges, we propose the ChordPrompt framework, which facilitates a harmonious interplay between visual and textual prompts. ChordPrompt introduces cross-modal prompts to leverage interactions between visual and textual information. Our approach also employs domain-adaptive text prompts to select appropriate prompts for continual adaptation across multiple domains. Comprehensive experiments on multi-domain incremental learning benchmarks demonstrate that ChordPrompt outperforms state-of-the-art methods in zero-shot generalization and downstream task performance.