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Hydrophobic and hydrophilic interactions are two major intermolecular forces between hydrophobic nonpolar and hydrophilic polar sites of macromolecules or materials surfaces in solvents. To further understand these two interactions at the microscopic level, an idealized polyatomic model is devised, which includes hydrophobic, hydrophilic, and partially hydrophilic polyatomic planar square molecular sheets. The hydrophobic molecular sheet is composed of the Lennard-Jones particles while the hydrophilic molecular sheet consists of positive and negative charge sites. In the framework of the extended reference interaction site model integral equation theory the solvent-induced interactions (or the potential of mean forces) between two parallel molecular sheets in water and in the hypothetical nonpolar water are investigated in a systematic fashion. Such a highly idealized model allows us to isolate and to explore the important effects of molecular size, relative intermolecular position (e.g., in- or out-of-registry configuration), and hydrophilic site distribution on the hydrophobic and hydrophilic interactions in both water and the hypothetical nonpolar water. Significant insight into these effects at the molecular level is obtained. For the hydrophobic planar molecules in water we find solvent separated hydrophobic interaction becomes less favored as sheet size increases. Moreover, the contact hydrophobic interaction between two molecular sheets in the out-of-registry configuration is always most favorable. For the latter case we find it is the van der Waals attraction, rather than the hydrophobic attraction, that dominates the total interaction. We also find that in both water and the hypothetical nonpolar water the solvent-induced interaction between two hydrophobic sheets behaves similarly. One possible explanation is that the hydrophobic hydration originating from the hydrogen bonding network in water plays an insignificant role in the solvent-induced interaction, at least in the infinitely dilute aqueous solution. For hydrophilic planar molecular sheets in water, we find water-induced hydrophilic interaction is much more substantial compared with the hydrophobic one. In many cases, the hydrophilic interaction is found directly against the intermolecular force between two parallel molecular sheets in vacuum. Finally, for the partially hydrophilic planar molecules in water, a newly discovered feature is that a disperse hydrophilic site distribution gives rise to stronger solvent-induced interaction compared with the clustered hydrophilic site distribution.