  It has been hypothesized that photons from young, massive star clusters are
responsible for maintaining the ionization of diffuse warm ionized gas seen in
both the Milky Way and other disk galaxies. For a theoretical investigation of
the warm ionized medium (WIM), it is crucial to solve radiation transfer
equations where the ISM and clusters are modeled self-consistently. To this
end, we employ a Solar neighborhood model of TIGRESS, a magnetohydrodynamic
simulation of the multiphase, star-forming ISM, and post-process the simulation
with an adaptive ray tracing method to transfer UV radiation from star
clusters. We find that the WIM volume filling factor is highly variable, and
sensitive to the rate of ionizing photon production and ISM structure. The mean
WIM volume filling factor rises to ~0.15 at |z|~1 kpc. Approximately half of
ionizing photons are absorbed by gas and half by dust; the cumulative ionizing
photon escape fraction is 1.1%. Our time-averaged synthetic H$\alpha$ line
profile matches WHAM observations on the redshifted (outflowing) side, but has
insufficient intensity on the blueshifted side. Our simulation matches the
Dickey-Lockman neutral density profile well, but only a small fraction of
snapshots have high-altitude WIM density consistent with Reynolds Layer
estimates. We compute a clumping correction factor C = <n_e>/sqrt<n_e^2>~0.2
that is remarkably constant with distance from the midplane and time; this can
be used to improve estimates of ionized gas mass and mean electron density from
observed H$\alpha$ surface brightness profiles in edge-on galaxies.
