We develop a mathematical model of nanoparticles depositing onto and penetrating into a biofilm grown in a parallel-plate flow cell. We carry out deposition experiments in a flow cell to support the modeling. The modeling and the experiments are motivated by the potential use of polymer nanoparticles as part of a treatment strategy for killing biofilms infecting the deep passages in the lungs. In the experiments and model, a fluid carrying polymer nanoparticles is injected into a parallel-plate flow cell in which a biofilm has grown over the bottom plate. The model consists of a system of transport equations describing the deposition and diffusion of nanoparticles. Standard asymptotic techniques that exploit the aspect ratio of the flow cell are applied to reduce the model to two coupled partial differential equations. We perform numerical simulations using the reduced model. We compare the experimental observations with the simulation results to estimate the nanoparticle sticking coefficient and the diffusion coefficient of the nanoparticles in the biofilm. The distributions of nanoparticles through the thickness of the biofilm are consistent with diffusive transport, and uniform distributions through the thickness are achieved in about four hours. Nanoparticle deposition does not appear to be strongly influenced by the flow rate in the cell for the low flow rates considered.