Water-mediated ion transport through functional nanoporous materials depends on the dynamics of water-confined within a given nanostructured morphology. Here, we investigate H-bonding dynamics of interfacial water within a "normal" (Type I) lyotropic gyroid phase formed by a gemini dicarboxylate surfactant self-assembly using a combination of 2DIR spectroscopy and molecular dynamics simulations. Experiments and :simulations demonstrate that water dynamics in the normal gyroid phase is 1 order of magnitude slower than that in bulk water, due to specific interactions between water, the ionic surfactant headgroups, and counterions. Yet, the dynamics of water in the normal gyroid phase are faster than those of water confined in a reverse spherical micelle of a sulfonate surfactant, given that the water pool in the reverse micelle and the water, pore in the gyroid phase have roughly the same diameters. This difference in confined water dynamics likely arises from the significantly reduced curvature-induced frustration at the convex interfaces of the normal gyroid, as compared to the concave interfaces of a reverse spherical micelle. These detailed insights into confined water dynamics may guide the future design of artificial membranes that rapidly transport protons and other ions.