We investigate the interplay between starbursts and host galaxies by studying the structure and physical characteristics of the ionized gas surrounding the central starbursts in the two nearby galaxies NGC 5253 and NGC 5236. The two systems form a pair that presumably interacted about 1 Gyr ago. They represent very different galactic environments, NGC 5253 being a metal-poor dwarf and NGC 5236 being a metal-rich, massive, grand-design spiral. We present images of the starburst regions in these two galaxies in the light of the line emission [O III] H alpha, and [S II] and in continuum U, V, and R. For NGC 5253, the images are deep enough that we can detect faint H alpha arches and filaments out to similar to 1.9 kpc and CS nl filaments out to similar to 1 kpc from the main ionizing cluster. The ground-based line images are complemented with an archival HST Wide Field Planetary Camera 2 H beta image. Line ratio maps [O III]/H beta and [S II]/H alpha show that in the outer regions the diffuse ionized gas is partially excited by a nonphotoionization process (" shocks "). The "shocked" gas is mostly concentrated southwest of the galaxy's center, in coincidence with the position of H alpha bubbles and with extended soft X-ray emission. The H alpha emission from the shock-excited gas is approximate to 1%-2% of the total and approximate to 10%-20% of the diffuse ionized gas emission, although the mechanical input from the starburst would be sufficient to support a shocked H alpha luminosity similar to 3 times the observed one. About 80%-90% of the diffuse gas is consistent with being photoionized, requiring that about 10% of the ionizing photons escape from the starburst site. The starburst in NGC 5253 appears to be fed by gas infalling along the galaxy's optical minor axis, while hot gas expanding from the starburst has a preferential direction along the major axis. The results for NGC 5236 are less clear than for NGC 5253, as the images are not as deep. In the central region of NGC 5236, the H alpha image traces the U emission from the ionizing stars more closely than in NGC 5253; the emission-line ratio maps show very little or no evidence for presence of shock excitation. Very little or no ionized gas appears expanding from the center of the galaxy outward along the disk plane, and ionization is a local process. The starburst in NGC 5236 is thus more strongly confined than that in NGC 5253; the deeper gravitational-potential well of the more massive galaxy probably keeps the ionized gas near to the ionizing stars.