Supported intermembrane junctions, formed by rupture of giant unilamellar vesicles onto conventional supported lipid membranes, have recently emerged as model systems for the study of biochemical processes at membrane interfaces. Using intermembrane fluorescence resonance energy transfer and optical standing wave fluorescence interferometry, we characterize the nanometer-scale topography of supported intermembrane junctions and find two distinct association states. In one state, the two membranes adhere in close apposition, with intermembrane separations of a few nanometers. In the second state, large intermembrane spacings of approximately 50 nm are maintained by a balance between Helfrich (entropic) repulsion and occasional sites of tight adhesion that pin the two membranes together. Reversible transitions between these two states can be triggered with temperature changes. We further examine the physical properties of membranes in each state using a membrane mixture near its miscibility phase transition temperature. Thermodynamic characteristics of the phase transition and diffusive mobility of individual lipids are comparable. However, collective Brownian motion of phase-separated domains and compositional fluctuations are substantially modulated by intermembrane spacing. The scaling properties of diffusion coefficient with particle size are determined from detailed analysis of domain motion in the different junction types. The results provide experimental verification of a theoretical model for two-dimensional mobility in membranes, which includes frictional coupling across an interstitial water layer.