A confined bilayer of water is studied at different temperatures and densities by classical and {\em ab initio} molecular dynamics simulations. At high density, hydrogen disorder is found to be behind the reported continuous phase transition. We observe the existence of a hexatic phase, suggesting that the Kosterlitz-Thouless-Halperin-Nelson-Young theory of a defect-mediated 2D crystal melting occurs. The liquid at different densities maintains the basic structure of the triangular ice. The two layers of liquid at high density show a strong correlation between one another without exchange of matter.