In an attempt to elucidate the remarkable stability of foams generated from dispersions of partially hydrophobic nanoparticles (fumed silica), we present investigations into the static and dilational properties of the gas-liquid interfaces of such dispersions. By relating the dynamic surface tension gamma(t) and the dilational elasticity E measured using an oscillating bubble device, we confirm that the Gibbs stability criterion E > gamma/2 against foam coarsening is fulfilled. We complement these studies using ellipsometry and Brewster angle microscopy, which provide evidence for a pronounced adsorption barrier for the particles and a network-like structure in the interface at sufficiently high concentrations. We observe this structure als...