  We simulate an isolated, magnetised Milky Way-like disc galaxy using a
self-consistent model of unresolved star formation and feedback, evolving the
system until it reaches statistical steady state. We show that the
quasi-steady-state structure is distinctly layered in galactocentric height
$z$, with an innermost region having comparable gas and magnetic pressures
(plasma beta $\beta \sim 1$), an outermost region having dominant gas pressures
($\beta \gg 1$), and an intermediate region between $300$ pc $\lesssim |z|
\lesssim 3$ kpc that is dynamically dominated by magnetic fields ($\beta \ll
1$). We find field strengths, gas surface densities, and star formation rates
that agree well with those observed both in the Galactic centre and in the
Solar neighbourhood. The most significant dynamical effect of magnetic fields
on the global properties of the disc is a reduction of the star formation rate
by a factor of 1.5-2 with respect to an unmagnetised control simulation. At
fixed star formation rate, there is no significant difference in the mass
outflow rates or profiles between the magnetised and non-magnetised
simulations. Our results for the global structure of the magnetic field have
significant implications for models of cosmic ray-driven winds and cosmic-ray
propagation in the Galaxy, and can be tested against observations with the
forthcoming Square Kilometre Array and other facilities. Finally, we report the
discovery of a physical error in the implementation of neutral gas heating and
cooling in the popular GIZMO code, which may lead to qualitatively incorrect
phase structures if not corrected.
