  Widespread, high altitude, diffuse ionized gas with scale heights of around a
kiloparsec is observed in the Milky Way and other star forming galaxies.
Numerical radiation-magnetohydrodynamic simulations of a supernova-driven
turbulent interstellar medium show that gas can be driven to high altitudes
above the galactic midplane, but the degree of ionization is often less than
inferred from observations. For computational expediency, ionizing radiation
from massive stars is often included as a post-processing step assuming
ionization equilibrium. We extend our simulations of a Milky Way-like
interstellar medium to include the combined effect of supernovae and
photoionization feedback from midplane OB stars and a population of hot evolved
low mass stars. The diffuse ionized gas has densities below 0.1 ${\rm
cm^{-3}}$, so recombination timescales can exceed millions of years. Our
simulations now follow the time-dependent ionization and recombination of low
density gas. The long recombination timescales result in diffuse ionized gas
that persists at large altitudes long after the deaths of massive stars that
produce the vast majority of the ionized gas. The diffuse ionized gas does not
exhibit the large variability inherent in simulations that adopt ionization
equilibrium. The vertical distribution of neutral and ionized gas is close to
what is observed in the Milky Way. The volume filling factor of ionized gas
increases with altitude resulting in the scale height of free electrons being
larger than that inferred from H$\alpha$ emission, thus reconciling the
observations of ionized gas made in H$\alpha$ and from pulsar dispersion
measurements.
