The preferential orientation of the water molecules near the water/1,2-dichloroethane interface is analyzed in detail at different distances from the interface on the basis of a grand canonical ensemble Monte Carlo simulation. The orientation of the individual water molecules is described by the angular polar coordinates of the interface normal vector in a local coordinate frame fixed to the particular water molecule, and the bivariate joint distribution of the two polar angles is calculated. It is found that water molecules have two distinct orientational preferences, and these two preferences exist simultaneously among the water molecules penetrating farthest into the organic phase. In the first preferred orientation the plane of the molecule is parallel to the interface, whereas in the second the molecular plane is aligned perpendicularly to the interface and the molecular dipole vector declines from the plane parallel to the interface by about 30degrees pointing toward the organic phase. The first of the two preferred orientations is found to be present in the entire interfacial region and also, to a smaller extent, in the subsurface water layer adjacent to the interface. The second orientational preference is only present among the water molecules penetrating farthest into the organic phase. The two orientations correspond to the alignment of a hydrogen bonded pair of water molecules, in which the molecule located toward the aqueous phase has the first, whereas the one on the organic side the second of the two preferred orientations. The obtained picture is in a clear contrast with the findings of previous studies, in which the orientation of the water molecules was described by monovariate distributions of the alignment of one or more selected molecule-fixed vectors. In order to understand the origin of the difference between the present results and earlier findings we also calculate the monovariate distributions of the direction of three of such molecular vectors, i.e., the dipole vector of the water molecule, the vector joining the two H atoms, and the vector perpendicular to the molecular plane. The comparison of the obtained monovariate distributions with the bivariate joint distribution of the two polar angles reveals that the averaging of the bivariate distribution over any of its two angles completely obscures the dual orientational preference. The present study clearly points out the importance of choosing appropriate statistical distributions in the analysis of simulation results and demonstrates the pitfalls of averaging over too many variables.