Tuned Mass Dampers (TMDs) exhibit high vibration reduction efficiency but narrow suppression bandwidth, while Vibro-Impact Nonlinear Energy Sinks (VI-NES) offer broad bandwidth yet relatively lower vibration efficiency. To concurrently address these limitations, this paper proposes a novel coupled vibration suppression system integrating TMD and VI-NES, synergistically leveraging their complementary advantages to achieve superior damping characteristics. First, the research develops a dynamic model of the coupled system, deriving semi-analytical results via the multi-scale method. Numerical validation confirms the accuracy of the semi-analytical results and identifies four distinct response mechanisms: chaos, symmetric collision, asymmetric collision, and multiple collision. Then, a parametric matching methodology is established for the coupled system, with comprehensive analysis of dynamic response characteristics and vibration suppression performance. Finally, research demonstrate that under equal subsystem mass ratios, the coupled system outperforms both standalone TMD and VI-NES systems in both vibration reduction efficiency and suppression bandwidth, validating its engineering superiority.