A discrete model is proposed to explain experimentally measured oscillatory disjoining pressure isotherms. The model uses concepts from an earlier model proposed by Tarazona and Vicente (Mol. Phys.56, 557, 1985). This approach yields oscillations with period equal to exactly two molecular diameters, which is contrary to all reported experimental data. When, instead of the simplest lattice-gas description, the Sanchez-Lacombe model (J. Phys. Chem.80, 2352, 1976) is used and a molecule is allowed to occupy several lattice sites, the period agrees well with experiments. Another new feature of our model is that, instead of accounting for only nearest-neighbor repulsion, it also allows for attractive next-nearest-neighbor interactions. The model has one adjustable parameter which is used to match experimental data on oscillatory solvation forces. A generalization of the Deryagin approximation to the case when structural forces are estimated using a density functional model is obtained.