Multi-agent reinforcement learning (MARL) methods often suffer from high sample complexity, limiting their use in real-world problems where data is sparse or expensive to collect. Although latent-variable world models have been employed to address this issue by generating abundant synthetic data for MARL training, most of these models cannot encode vital global information available during training into their latent states, which hampers learning efficiency. The few exceptions that incorporate global information assume centralized execution of their learned policies, which is impractical in many applications with partial observability. We propose a novel model-based MARL algorithm, MABL (Multi-Agent Bi-Level world model), that learns a bi-level latent-variable world model from high-dimensional inputs. Unlike existing models, MABL is capable of encoding essential global information into the latent states during training while guaranteeing the decentralized execution of learned policies. For each agent, MABL learns a global latent state at the upper level, which is used to inform the learning of an agent latent state at the lower level. During execution, agents exclusively use lower-level latent states and act independently. Crucially, MABL can be combined with any model-free MARL algorithm for policy learning. In our empirical evaluation with complex discrete and continuous multi-agent tasks including SMAC, Flatland, and MAMuJoCo, MABL surpasses SOTA multi-agent latent-variable world models in both sample efficiency and overall performance.