  Understanding how the Galactic magnetic field threads the multi-phase
interstellar medium (ISM) remains a considerable challenge, as different
magnetic field tracers probe dissimilar phases and field components. We search
for evidence of a common magnetic field shared between the ionized and neutral
ISM by comparing 1.4 GHz radio continuum polarization and HI line emission from
the Galactic Arecibo L-Band Feed Array Continuum Transit Survey (GALFACTS) and
Galactic Arecibo L-Band Feed Array HI (GALFA-HI) survey, respectively. We
compute the polarization gradient of the continuum emission and search for
associations with diffuse/translucent HI structures. The polarization gradient
is sensitive to changes in the integrated product of the thermal electron
density and line-of-sight field strength ($B_\parallel$) in warm ionized gas,
while narrow HI structures highlight the plane-of-sky field orientation in cold
neutral gas. We identified one region in the high-Galactic latitude Arecibo
sky, G216+26 centered on $(\ell,b)\sim(216\deg,+26\deg)$, containing filaments
in the polarization gradient that are aligned with narrow HI structures roughly
parallel to the Galactic plane. We present a comparison of multi-phase
observations and magnetic field tracers of this region, demonstrating that the
warm ionized and cold neutral media are connected likely via a common magnetic
field. We quantify the physical properties of a polarization gradient filament
associated with H$\alpha$ emission, measuring a line-of-sight field strength
$B_\parallel=6{\pm}4 \mu$G and a plasma beta $\beta=2.1^{+3.1}_{-2.1}$. We
discuss the lack of widespread multi-phase magnetic field alignments and
consider whether this region is associated with a short-timescale or physically
rare phenomenon. This work highlights the utility of multi-tracer analyses for
understanding the magnetized ISM.
