Neutron reflectivity was used to study the interdiffusion of thin film bilayers of cross-linked deuterated and protonated polystyrene. The films were spun-cast and cross-linked by gamma radiation. Interfacial broadening was studied as a function of annealing time for different cross-link densities. The samples were annealed in a vacuum at 150 degreesC, and neutron reflectivity measurements were performed in air at room temperature. The interface was observed to broaden rapidly at short annealing times and then plateau to an equilibrium value. The interfacial broadening was modeled using a solution to the Fokker-Planck equation with a parabolic external potential to obtain the equilibrium interfacial width and effective diffusion coeffcient as a function of the average network mesh size, (N) over bar (c),. The interfacial width was found to scale as (N) over bar (0.47+/-0.1)(c). The effective diffusion coefficient was found to be independent of (N) over bar (c).