Hydrophobicity/hydrophilicity of aqueous interfaces at the molecular level results from a subtle balance in the water-water and water-surface interactions. This is characterized here via density functional theory-molecular dynamics (DFT-MD) coupled with vibrational sum frequency generation (SFG) and THz-IR absorption spectroscopies. We show that water at the interface with a series of weakly interacting materials is organized into a two-dimensional hydrogen-bonded network (2D-HB-network), which is also found above some macroscopically hydrophilic silica and alumina surfaces. These results are rationalized through a descriptor that measures the number of "vertical" and "horizontal" hydrogen bonds formed by interfacial water, quantifying the competition between water-surface and water-water interactions. The 2D-HB-network is directly revealed by THz-IR absorption spectroscopy, while the competition of water-water and water-surface interactions is quantified from SFG markers. The combination of SFG and THz-IR spectroscopies is thus found to be a compelling tool to characterize the finest details of molecular hydrophobicity at aqueous interfaces.