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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 mid-plane, 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 an Milky Way-like interstellar medium to include the combined effect of supernovae and photoionization feedback from mid-plane 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 time-scales can exceed millions of years. Our simulations now follow the time-dependent ionization and recombination of low density gas. The long recombination time-scales 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. [ABSTRACT FROM AUTHOR]