The swelling behavior of surface-anchored poly(N-isopropylacrylamide) (polyNIPAAm) networks in D₂O has been characterized with neutron reflection and compared to the demixing behavior of linear poly(NIPAAm) in solution. The surface-anchored networks were prepared from photo-cross-linkable poly(NIPAAm) copolymers with benzophenone-pendant monomers. Neutron reflection measurements reveal that the discontinuity in the volume transition of the surface-tethered networks coincides with the miscibility gap of poly(NIPAAm) solutions. This result perhaps signifies that the Flory interaction parameter,χ, of poly(NIPAAm) in water is unaffected by cross-linking and can be used to model volume-phase transitions in constrained systems. We consequently show that by varying only the cross-link density, the surface-anchored networks can undergo either a continuous or a discontinuous transition. Above a critical cross-link density, the network is prohibited from entering the miscibility gap of poly(NIPAAm), and moves from a swollen state to a less swollen state in a relatively continuous manner. Moreover, using a composition and temperature dependent Flory interaction parameter,χ(φ,T), tabulated from the demixing data of linear poly(NIPAAm), the swelling behavior of the surface-tethered networks can be modeled using the mean-field Flory-Rehner theory modified for uniaxial swelling.