Disordered mesoporous materials with pore sizes ranging from 2 nm to some 10 nm develop large specific surface areas. These matrices can be easily filled with polar fluids And the interfacial region between the solid matrix and the pore network strongly influences the molecular dynamics of the entrapped fluid. A promising way to probe such a coupling on a large time-scale is to look at the dispersion of the nuclear spin-lattice relaxation rate of the polar liquid using field cycling NMR relaxometry technique. We have performed such an experiment on a fully hydrated porous Vycor glass, free of electron paramagnetic impurities. The proton nuclear magnetic relaxation rate (1/T1) exhibits a logarithmic dependence on Larmor frequency over the range from 0.01 to 30 MHz. A cross-over is observed below 0.1 MHz. In order to understand the relationship between geometric disorder, interfacial confinement, and nuclear magnetic relaxationdispersion (NMRD), we first compute an off-lattice reconstruction of the Vycor glass This model agrees with available experimental data (specific surface, porosity, chord length distributions, small angle scattering and tortuosity). A Brownian dynamics simulation is performed to analyze long time molecular self-diffusion and NMRD data. These later are well reproduced and appear to be connected with the translation diffusion of water near the SiO2 interface. The logarithmic character of the NMRD is specifically related to the interfacial geometry of the Vycor glass. Several other multiconnected interfacial structures such as periodic minimal surfaces do not exhibit such an evolution. Therefore, NMRD appears to be selectively sensitive to the interfacial geometry of mesoscopic disordered materials (MDM).