We elaborate a hybrid fluid-kinetic model for neutral particles in the plasma edge. A macro/fluid model with kinetic corrections in the closure terms of the fluid moment equations is solved in the entire domain. The kinetic corrections follow from a Monte Carlo simulation of the micro/kinetic part. We compare two hybrid models with different underlying fluid approximations: (i) a pure pressure-diffusion equation; and (ii) a continuity and parallel momentum equation with pressure-diffusion transport only retained in the directions perpendicular to the magnetic field lines. We asses their performance for a high recycling slab case with fixed background plasma. Compared to a Monte Carlo simulation of the full kinetic equation, the statistical error on the particle source is reduced with 40% and 47% for respectively the hybrid model without and with the parallel momentum equation for the same computational time. For the parallel momentum source there is only a reduction for the model with parallel momentum equation (about 69%). Unfortunately, the statistical error on the ion energy source slightly increases for both hybrid models. Keywords: Fluid approximations, Kinetic model, Neutrals, Plasma edge modeling