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 primarys 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 systems age and how HD 1160 B fits within the context of (sub)stellar evolution.
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