Water-solid interactions are of broad importance both in nature and technology. The hexagonal bilayer model based on the Bernal-Fowler-Pauling ice rules has been widely adopted to describe water structuring at interfaces. Using a cryogenic scanning tunnelling microscope, here we report a new type of two-dimensional ice-like bilayer structure built from cyclic water tetramers on an insulating NaCl(001) film, which is completely beyond this conventional bilayer picture. A novel bridging mechanism allows the interconnection of water tetramers to form chains, flakes and eventually a two-dimensional extended ice bilayer containing a regular array of Bjerrum D-type defects. Ab initio density functional theory calculations substantiate this bridging growth mode and reveal a striking proton-disordered ice structure. The formation of the periodic Bjerrum defects with unusually high density may have a crucial role as H donor sites in directing multilayer ice growth and in catalysing heterogeneous chemical reactions on water-coated salt surfaces.