Balance control is important for human and bipedal robotic systems. While dynamic balance during locomotion has received considerable attention, quantitative understanding of static balance and falling remains limited. This work presents a hierarchical control pipeline for simulating human balance via a comprehensive whole-body musculoskeletal system. We identified spatiotemporal dynamics of balancing during stable standing, revealed the impact of muscle injury on balancing behavior, and generated fall contact patterns that aligned with clinical data. Furthermore, our simulated hip exoskeleton assistance demonstrated improvement in balance maintenance and reduced muscle effort under perturbation. This work offers unique muscle-level insights into human balance dynamics that are challenging to capture experimentally. It could provide a foundation for developing targeted interventions for individuals with balance impairments and support the advancement of humanoid robotic systems.