Integrating wave energy converters (WECs) on an offshore wind platform provides an economic and robust solution for co-located wind and wave power exploitation. The power performance of the hybrid system depends on the hydrodynamic interactions between the platform and WECs, but most of these effects remain unclear. In this study, through a hybrid system consisting of a semi-submersible platform and heaving point absorber WECs, this matter is addressed based on the higher-order boundary element method and multi-body constrained dynamics. Results show that a new prominent power peak appears while the platform and WECs are in a so-called synchronized mode regardless of the layout of the WECs, wherein the power of a single WEC can be increased by up to 41.4% and the total power by up to 26.7% and the heave motion of the platform increases. Out of the vicinity of the synchronized mode frequency, the WECs have a small impact on the surge motion and pitch motion of the platform, whereas reducing its resonant heave motion at the natural frequency. This work reveals useful insights into the dynamic and power performance of a wind-wave hybrid system, providing detailed configurations and potential guidance for the practical design and application.