We have demonstrated that with a composite nanoporous ceramic membrane in a batch membrane cell it is technically feasible to switch off the trans-membrane hydrostatic pressure difference within tens of milliseconds. That enabled us to resolve practically the whole time evolution of transient filtration potential. Measurements of the latter have been complemented by measurements of steady-state salt rejection by the composite membrane and by measurements of the streaming potential and hydraulic permeability of membrane supports available separately. A theory has been developed in terms of network thermodynamics for the electrical response of a bilayer membrane to a pressure perturbation. In combination with the results of salt rejection measurements, from the time transients of filtration potential we could determine the ion transport numbers within the nanoporous layer. Besides that, from the dependence of steady-state salt rejection on the trans-membrane volume flow, we have determined the diffusion permeability of and the salt reflection coefficient in the nanoporous layer. This has enabled us to estimate the contributions of Donnan and non-Donnan mechanisms to the rejection of ions by the nanoporous membrane used in this study. It has been unexpectedly found that the Donnan exclusion played only a secondary role. Our hypothesis is that the non-Donnan exclusion of ions from the nanopores might be caused by changes in water properties in nanoconfinement. Proceeding from the results of steady-state filtration experiments with the membrane and the support, we also concluded that the nanoporous layer was imperfection-free and had a quite narrow pore size distribution, which made it a suitable object for fundamental studies of ion transfer mechanisms in nanopores.