Recently determined atomistic scale structures of near-two dimensional bilayers of vitreous silica (using scanning probe and electron microscopy) allow us to refine the experimentally determined coordinates to incorporate the known local chemistry more precisely. Further refinement is achieved by using classical potentials of varying complexity; one using harmonic potentials and the second employing an electrostatic description incorporating polarization effects. These are benchmarked against density functional calculations. Our main findings are that (a) there is a symmetry plane between the two disordered layers; a nice example of an emergent phenomenon, (b) the layers are slightly tilted so that the Si-O-Si angle between the two layers is not ${180^{\circ}}$ as originally thought but rather ${175 \pm 2 ^\circ}$ and (c) while interior areas that are not completely imagined can be reliably reconstructed, surface areas are more problematical. It is shown that small crystallites that appear are just as expected statistically in a continuous random network. This provides a good example of the value that can be added to disordered structures imaged at the atomic level by implementing computer refinement.