Electrostatic-charge accumulation and discharge can cause a variety of problems in imaging, electronic, and packaging materials and processes. Nanoparticulate antimony-doped tin oxide containing antistatic layers provide robust electronic conductivity that survives aqueous and thermal processing. Dielectric spectroscopy of tin oxide-gelatin (antistatic) thin films reveals relaxation processes that depend on tin oxide-to-gelatin ratios and upon tin oxide-gelatin film thickness. The frequency maxima of dielectric-loss peaks inversely correlate with surface electrical resistance (SER) measurements. A simple model of a layered heterogeneous dielectric explains the relative position of dielectric-loss peaks in terms of antistatic-layer conductivity. Dielectric measurements of antistatic layers do not require ohmic contact with such layers, and measurements on "buried layers" are straightforward. An observation of apparent percolation induced by variations in coverage, at constant tin oxide-to-gelatin weight ratio, suggests that the coating conditions and drying processes appear to play a role in network formation and nanoparticulate aggregation. Scaling of (inverse) SER and dielectric-loss peak frequencies above the percolation threshold conforms with scaling expected for electrical-conductivity percolation in three dimensions.