It is proposed that turbulent mixing layers are common in the ISM of the Milky Way and selected external galaxies, with many layers per kiloparsec along typical lines of sight. All of the diffuse C I 1550-A background emission and a significant fraction of the diffuse H-alpha background at high latitude can be explained by mixing layers cooling at pressure of about 3000/cu cm K. These models also produce the correct ratio of semiforbidden C IV 15500 III 1663-A emission. Only 10 percent of the disk H-alpha is likely to arise from mixing layers. The observed Galactic absorption-line column densities of C IV, N V, Si IV, and O VI are roughly consistent with mixing-layer models with an intermediate temperature of about 10 exp 5.3 K and depleted abundances.