  Magnetic fields permeate the diffuse interstellar medium (ISM) of the Milky
Way, and are essential to explain the dynamical evolution and current shape of
the Galaxy. Magnetic fields reveal themselves via their influence on the
surrounding matter, and as such are notoriously hard to measure independently
of other tracers. In this work, we attempt to disentangle an all sky map of the
line-of-sight parallel component of the Galactic magnetic field from the
Faraday effect, utilizing several tracers of the Galactic thermal electron
density. Additionally, we aim to produce a Galactic electron dispersion measure
map and quantify several tracers of the structure of the ionized medium of the
Milky Way. We rely on compiled catalogs of extragalactic Faraday rotation
measures and Galactic pulsar dispersion measures, a well as data on
bremsstrahlung and the hydrogen $\alpha$ spectral line to trace the ionized
medium of the Milky Way. We present the first full sky map of the line-of-sight
averaged Galactic magnetic field. Within this map, we find LoS parallel and
LoS-averaged magnetic field strengths of up to 4 $\mu$G, with an all-sky
root-mean-square of 1.1 $\mu$G, which is consistent with previous local
measurements and global magnetic field models. Additionally, we produce a
detailed electron dispersion measure map, which agrees with already existing
parametric models at high latitudes, but suffers from systematic effects in the
disk. Further analysis of our results with regard to the 3D structure of
$n_{th}$ reveals that it follows a Kolmogorov-type turbulence for most of the
sky. From the reconstructed dispersion measure and emission measure maps we
construct several tracers of variability of $n_{th}$ along the LoS.
