Widespread, high altitude, diffuse ionized gas with scale heights of around akiloparsec is observed in the Milky Way and other star forming galaxies.Numerical radiation-magnetohydrodynamic simulations of a supernova-driventurbulent interstellar medium show that gas can be driven to high altitudesabove the galactic midplane, but the degree of ionization is often less thaninferred from observations. For computational expediency, ionizing radiationfrom massive stars is often included as a post-processing step assumingionization equilibrium. We extend our simulations of a Milky Way-likeinterstellar medium to include the combined effect of supernovae andphotoionization feedback from midplane OB stars and a population of hot evolvedlow mass stars. The diffuse ionized gas has densities below 0.1 ${\rmcm^{-3}}$, so recombination timescales can exceed millions of years. Oursimulations now follow the time-dependent ionization and recombination of lowdensity gas. The long recombination timescales result in diffuse ionized gasthat persists at large altitudes long after the deaths of massive stars thatproduce the vast majority of the ionized gas. The diffuse ionized gas does notexhibit the large variability inherent in simulations that adopt ionizationequilibrium. The vertical distribution of neutral and ionized gas is close towhat is observed in the Milky Way. The volume filling factor of ionized gasincreases with altitude resulting in the scale height of free electrons beinglarger than that inferred from H$\alpha$ emission, thus reconciling theobservations of ionized gas made in H$\alpha$ and from pulsar dispersionmeasurements.