In order to understand the formation and evolution of Magellanic-type dwarf irregular (dIm) galaxies, one needs to understand their three-dimensional structure. We present measurements of the stellar velocity dispersion in NGC1569, a nearby post-starburst dIm galaxy. The stellar vertical velocity dispersion, σ z, coupled with the maximum rotational velocity derived from H I observations, V max, gives a measure of how kinematically hot the galaxy is, and, therefore, indicates its structure. We conclude that the stars in NGC1569 are in a thick disk with a V max/σ z = 2.4 ± 0.7. In addition to the structure, we analyze the ionized gas kinematics from O III observations along the morphological major axis. These data show evidence for outflow from the inner starburst region and a potential expanding shell near supermassive star cluster (SSC) A. When compared to the stellar kinematics, the velocity dispersion of the stars increases in the region of SSC A supporting the hypothesis of an expanding shell. The stellar kinematics closely follow the motion of the gas. Analysis of high-resolution H I data clearly reveals the presence of an H I cloud that appears to be impacting the eastern edge of NGC1569. Also, an ultra-dense H I cloud can be seen extending to the west of the impacting H I cloud. This dense cloud is likely the remains of a dense H I bridge that extended through what is now the central starburst area. The impacting H I cloud was the catalyst for the starburst, thus turning the dense gas into stars over a short timescale, ∼1Gyr. We performed a careful study of the spectral energy distribution using infrared, optical, and ultraviolet photometry, producing a state-of-the-art mass model for the stellar disk. This mass modeling shows that stars dominate the gravitational potential in the inner 1kpc. The dynamical mass of NGC1569, derived from V max, shows that the disk may be dark matter deficient in the inner region, although, when compared to the expected virial mass determined from halo abundance matching techniques, the dark matter profile seems to agree with the observed mass profile at a radius of 2.2kpc. © 2012. The American Astronomical Society. All rights reserved.