The task of item-to-item (I2I) retrieval is to identify a set of relevant and highly engaging items based on a given trigger item. It is a crucial component in modern recommendation systems, where users' previously engaged items serve as trigger items to retrieve relevant content for future engagement. However, existing I2I retrieval models in industry are primarily built on co-engagement data and optimized using the recall measure, which overly emphasizes co-engagement patterns while failing to capture semantic relevance. This often leads to overfitting short-term co-engagement trends at the expense of long-term benefits such as discovering novel interests and promoting content diversity. To address this challenge, we propose MTMH, a Multi-Task and Multi-Head I2I retrieval model that achieves both high recall and semantic relevance. Our model consists of two key components: 1) a multi-task learning loss for formally optimizing the trade-off between recall and semantic relevance, and 2) a multi-head I2I retrieval architecture for retrieving both highly co-engaged and semantically relevant items. We evaluate MTMH using proprietary data from a commercial platform serving billions of users and demonstrate that it can improve recall by up to 14.4% and semantic relevance by up to 56.6% compared with prior state-of-the-art models. We also conduct live experiments to verify that MTMH can enhance both short-term consumption metrics and long-term user-experience-related metrics. Our work provides a principled approach for jointly optimizing I2I recall and semantic relevance, which has significant implications for improving the overall performance of recommendation systems.