  We present high signal-to-noise ratio, precise $YJH$ photometry and $Y$ band
(\gpiwave~$\mu$m) spectroscopy of HD 1160 B, a young substellar companion
discovered from the Gemini NICI Planet Finding Campaign, using the Subaru
Coronagraphic Extreme Adaptive Optics instrument and the Gemini Planet Imager.
HD 1160 B has typical mid-M dwarf-like infrared colors and a spectral type of
M5.5$^{+1.0}_{-0.5}$, where the blue edge of our $Y$ band spectrum rules out
earlier spectral types. Atmospheric modeling suggests HD 1160 B having an
effective temperature of 3000--3100 $K$, a surface gravity of log $g$ = 4--4.5,
a radius of~\bestfitradius~$R_{\rm J}$, and a luminosity of log $L$/$L_{\odot}
= -2.76 \pm 0.05$. Neither the primary's Hertzspring-Russell diagram position
nor atmospheric modeling of HD 1160 B show evidence for a sub-solar
metallicity. The interpretation of the HD 1160 B depends on which stellar
system components are used to estimate an age. Considering HD 1160 A, B and C
jointly, we derive an age of 80--125 Myr, implying that HD 1160 B straddles the
hydrogen-burning limit (70--90 $M_{\rm J}$). If we consider HD 1160 A alone,
younger ages (20--125 Myr) and a brown dwarf-like mass (35--90 $M_{\rm J}$) are
possible. Interferometric measurements of the primary, a precise GAIA parallax,
and moderate resolution spectroscopy can better constrain the system's age and
how HD 1160 B fits within the context of (sub)stellar evolution.
