Medical visual question answering (Med-VQA) is a crucial multimodal task in clinical decision support and telemedicine. Recent self-attention based methods struggle to effectively handle cross-modal semantic alignments between vision and language. Moreover, classification-based methods rely on predefined answer sets. Treating this task as a simple classification problem may make it unable to adapt to the diversity of free-form answers and overlook the detailed semantic information of free-form answers. In order to tackle these challenges, we introduce a Cross-Mamba Interaction based Multi-Task Learning (CMI-MTL) framework that learns cross-modal feature representations from images and texts. CMI-MTL comprises three key modules: fine-grained visual-text feature alignment (FVTA), cross-modal interleaved feature representation (CIFR), and free-form answer-enhanced multi-task learning (FFAE). FVTA extracts the most relevant regions in image-text pairs through fine-grained visual-text feature alignment. CIFR captures cross-modal sequential interactions via cross-modal interleaved feature representation. FFAE leverages auxiliary knowledge from open-ended questions through free-form answer-enhanced multi-task learning, improving the model's capability for open-ended Med-VQA. Experimental results show that CMI-MTL outperforms the existing state-of-the-art methods on three Med-VQA datasets: VQA-RAD, SLAKE, and OVQA. Furthermore, we conduct more interpretability experiments to prove the effectiveness. The code is publicly available at https://github.com/BioMedIA-repo/CMI-MTL.