A recent experiment showed that when self-assembled monolayers of single-stranded DNA or PNA are exposed to water vapor, they first shrink and then swell with increasing humidity. In order to understand how a monolayer can shrink by absorbing water, we introduce a three-component lattice model consisting of polymer, water, and vacancies. We find that for moderate grafting densities, attractive monomer-water, and repulsive monomer monomer interactions, at low water vapor concentrations, the adsorption of water is accompanied by enhanced expulsion of vacancies and compression of the monolayer. As humidity is further increased, continued adsorption of water molecules leads to swelling of the monolayer. The low humidity anomaly is predicted to disappear at high grafting densities.