We demonstrate a method to measure both rotation curves and 3D ISM structure in edge-on galaxies. Two-dimensional spectral coverage of edge-on galaxies reveals substantial deviations in emission line shapes from a purely gaussian profile that vary with radius and height. Non-gaussianity is quantified using statistical moments to third order. We infer the 3D density distribution by comparing the measured line profiles to synthetic line-of-sight velocity distributions from a suite of three-dimensional galaxy models with different 3D distributions of dust and gas and different rotation curve shapes and amplitudes. We apply this method using multi-position longslit data of nearby edge-on galaxy ESO 435-G25 and find our derived rotation curve matches measured HI rotation from envelope fitting but requires a flared dust disk to accurately describe the radial and vertical trends in the measured statistical moments. Our results are consistent with dynamical expectations for constant pressure support in a disk with exponentially declining surface-density.