We provide a detailed description of the structure of water at the interface with the air (liquid-vapor LV interface) from state-of-the-art DFT-based molecular dynamics simulations. For the first time, a two-dimensional (2D) H-bond extended network has been identified and fully characterized, demonstrating that interfacial water is organized into a 2D sheet with H-bonds oriented parallel to the instantaneous surface and following its spatial and temporal oscillations. By analyzing the nonlinear vSFG (vibrational sum frequency generation) spectrum of the LV interface in terms of layer-by-layer signal, we demonstrate that the 2D water sheet is solely responsible for the spectral signatures, hence providing the interfacial 3.5 Å thickness effectively probed in nonlinear interfacial spectroscopy. The 2D H-bond network unraveled here is the essential key to rationalize macroscopic properties of water-air interfaces, as demonstrated here for spectroscopy and the surface potential.