We have calculated two-dimensional models for the global structure of the interstellar medium in a is galaxy where stars and gas are coupled through star formation, mass loss, stellar heating of the gas, and optically thin radiative cooling. In one set of models, the two dimensions are in the plane of a disk, and for one case, the total size of the region is 1 kpc square. Using a more accurate numerical approach, we confirm the results of Chiang & Bregman (1988) that the neutral gas (H I) forms into filaments or sheets separated by hotter, more diffuse gas. Although the filaments often have denser sub-regions, individual clouds of neutral gas are rare. We calculated the vertical distribution of the gas in another set of models where one dimension was in the plane and the other was perpendicular to it. A filament and hot gas network still occurs, although dense neutral complexes are more common and occur near the midplane. The hot gas often cools as it rises, leading to the highest velocity material having both positive and negative velocities. We find other features that are qualitatively similar to observations: the scale heights of the gas increase with increasing temperature, low-density regions have dimensions of 50-100 pc, and H I ''worms'' are produced.