The pore structure of an alumina membrane was studied by adsorption in conjunction with small-angle neutron scattering (SANS). The effect of an incomplete contrast matching was investigated and simple formulae allowing the calculation of the amount of water adsorbed and the film areas, at various relative pressures, were derived for the ternary system. In the vicinity of the contrast matching point, however, incomplete contrast matching does not introduce a substantial complication to data analysis. The adsorption isotherm was reconstructed from the SANS data and agrees well with the experimental adsorption isotherm. For the alumina membrane, a coordination number of approximate to 10 was estimated from the SANS determined areas.