Multi-energy microgrid (MEMG) has the potential to improve the energy utilization efficiency. However, the uncertainty caused by distributed renewable energy resources brings an urgent need for multi-energy co-optimization to ensure secure operation. This paper focuses on the distributionally robust energy management problem for MEMG. Various flexible resources in different energy sectors are utilized for uncertainty mitigation, then, a data-driven Wasserstein distance-based distributionally robust joint chance-constrained (DRJCC) energy management model is proposed. To make the DRJCC model tractable, an optimized conditional value-at-risk (CVaR) approximation (OCA) formulation is proposed to transfer the joint chance-constrained model into a tractable form. Then, an iterative sequential convex optimization algorithm is tailored to reduce the solution conservatism by tuning OCA. Numerical result illustrates the effectiveness of the proposed model.