Effective collaboration in multi-agent systems requires mechanisms for coordination and adaptability in dynamic and uncertain environments. However, existing multi-agent systems rarely model resilience explicitly, instead relying on ad-hoc output correction that limits systematic, runtime management of robustness. In this work, we propose Multi-Agent Mesh (MA-Mesh), a framework that constructs a role-based self-healing layer on top of a collaboration pattern. Specifically, MA-Mesh generates resilience-aware system specifications and synthesizes them into executable multi-agent policy code. To enhance resilience, we introduce two self-healing mechanisms: Cross-agent reflection, a mechanism that allows agents to evaluate not only their own outcomes but also the performance of their peers, enabling informed behavioral adjustments and collective policy refinement; Role-based failover, a strategy which dynamically reassigns roles and enables agents to substitute for one another when sub-tasks fail or agents underperform, ensuring continuity of task execution. Experimental results across diverse tasks (e.g., software development, tool use, scientific reasoning) demonstrate that MA-Mesh significantly outperforms existing multi-agent systems in both task performance and robustness under system uncertainty.