There is strong evidence that the diffuse ionized gas (DIG) in disc galaxies is photoionized by radiation from UV luminous O and B stars in the galactic disc, both from observations and detailed numerical models. However, it is still not clear what mechanism is responsible for providing the necessary pressure support for a diffuse gas layer at kpc-scale above the disc. In this work we investigate if the pressure increase caused by photoionization can provide this support. We run self-consistent radiation hydrodynamics models of a gaseous disc in an external potential. We find that photoionization feedback can drive low levels of turbulence in the dense galactic disc, and that it provides pressure support for an extended diffuse gas layer. Our results show that there is a natural fine-tuning between the total ionizing radiation budget of the sources in the galaxy and the amount of gas in the different ionization phases of the ISM, and provide the first fully consistent radiation hydrodynamics model of the DIG.