This paper focusses on the hydrodynamic performance of an unmanned vehicle system, consisting of a remotely operated underwater vehicle (ROV) that has to be launched and recovered autonomously from an Autonomous Surface Vehicles (ASV). The hydrodynamic model of the ASV/ROV coupled system is described in detail and solved numerically. The paper seeks to assess the overall performance of the ASV/ROV system, including the stability of the ASV, the ROV tidal current capacity and the required power of the launch and recovery winch system. The results demonstrate that this ASV/ROV system can complete the launch, holding and recovery tasks meeting stability for the given winch power requirements. The tidal current capacity of the ROV decreases with a larger target water depth. The maximum ROV umbilical tension is observed during steep wave instances when the ROV is in proximity to the ASV. A down-control force is demonstrated to be a suitable solution to limit the maximum tension within the umbilical rated force limits. This paper presents the methods and considerations for working towards a fully autonomous ASV/ROV system capable of autonomous inspection and maintenance missions. The work will be useful for practitioners and researcher working on autonomous offshore systems.