To shed light on the microscopic mechanism of hydrophobic hydration, we study a simplified lattice model for water solutions in which the orientational nature of hydrogen bonding as well as the degeneracy related to proton distribution are taken into account. Miscibility properties of the model are looked at for both polar (hydrogen bonding) and nonpolar (non-hydrogen bonding) solutes. A quasichemical solution for the pure system is reviewed and extended to include the different kinds of solute. A Monte Carlo study of our model yields a novel feature for the local structure of the hydration layer: energy correlation relaxation times for solvation water are larger than the corresponding relaxation times for bulk water. This result suggests the presence of ordering of water particles in the first hydration shell. A nonassociating model solvent, represented by a lattice gas, presents opposite behavior, indicating that this effect is a result of the directionality of the interaction. In presence of polar solutes, we find an ordered mixed pseudophase at low temperatures, indicating the possibility of closed loops of immiscibility.