Backscatter SEM imaging and small-angle neutron scattering (SANS) data are combined within a statistical framework to quantify the microstructure of a porous solid in terms of a continuous pore-size distribution spanning over five orders of magnitude of length scale, from 10 Angstrom to 500 mum. The method is demonstrated on a sample of natural sandstone and the results are tested against mercury porosimetry (MP) and nuclear magnetic resonance (NMR) relaxation data. The rock microstructure is fractal (D = 2.47) in the pore-size range 10 Angstrom - 50 mum and Euclidean for larger length scales. The pore-size distribution is consistent with that determined by MP. The NMR data show a bimodal distribution of proton T-2 relaxation times, which is interpreted quantitatively using a model of relaxation in fractal pores. Pore-length scales derived from the NMR data are consistent with the geometrical parameters derived from both the SEM/SANS and NIP data. The combined SANS/BSEM method furnishes new microstructural information that should facilitate the study of capillary phenomena in hydrocarbon reservoir rocks and other porous solids exhibiting broad pore-size distributions. (C) 2004 Elsevier Inc. All rights reserved.