Embodied planning is dedicated to the goal of building agents capable of perceiving, reasoning, and executing long-horizon tasks in physical environments. However, existing embodied benchmarks predominantly focus on single-agent execution or restricted multi-agent settings, leaving long-horizon tasks that involve complex inter-agent dependencies largely underexplored despite their prevalence in real-world embodied scenarios. To address this gap, we introduce CoEmbod, the first realistic 3D simulated embodied benchmark for long-horizon multi-agent embodied cooperation with diverse inter-agent dependencies. CoEmbod contains 155 expert-curated tasks across 40 scenes and 10845 objects, covering three cooperation regimes: spatial distribution, parallel constraint, and failure recovery. These regimes cover a broad spectrum of cooperative requirements, ranging from distributed task allocation to synchronized execution and assisted failure recovery. CoEmbod further provides a process-level evaluation framework with Budgeted Cooperative Success (BCS), which jointly measures goal completion, cooperation fidelity, and execution efficiency. Experiments reveal that even the leading LMM powering a well-established agentic workflow achieves only 20.23% success, highlighting the difficulty of long-horizon multi-agent cooperation with diverse inter-agent dependencies in complex embodied environments.