In nature, turbulent flows exist that are neither simply 2D nor 3D but are forced towards one state or the other by boundary conditions such as varying stratification. Here, we report the first evidence of the co-existence of an inverse and a direct energy cascade in an experimental flow driven by Faraday waves in water. We find that an inverse energy cascade at the fluid surface and a direct energy cascade in the 3D bulk flow underneath co-exist. We base our analysis on temporally and spatially well-resolved velocity fields obtained by particle image velocimetry measurements at planes parallel and perpendicular to the water surface. The findings also provide strong evidence that the intense turbulent 2D surface flow drives the 3D bulk flow through sporadic vertical jets as a source of momentum to the bulk liquid.