The symbiotic binary system MWC 560 (V694 Mon) consists of an M giant with an accreting white dwarf companion. The accretion disk produces a jet which is the only known case of a stellar jet oriented along our line of sight, a geometry which simplifies jet/disk modeling and thus makes MWC 560 a uniquely valuable test case of such systems. Past near-IR photometric monitoring has shown that even during outbursts the M giant dominates the IR SED. However, the only IR spectra of the M giant previous to this work had a resolution of R ~ 400. We present the first medium-resolution (R ~ 2000) spectrum of the symbiotic binary MWC 560 in April 2016 during the outburst, covering a spectral range from 0.7 micron to 2.5 microns. As expected, the IR continuum is dominated by the cool giant photosphere, with some emission features arising from other regions of the system. We derive the effective temperature of the giant using the strength of CO absorption bands. We discovered a strong photospheric ZrO absorption feature which implies that the cool giant is an S star (i.e., a giant enriched in s-process elements). Strong He I 1.083 micron absorption is observed which arises in the jet from the white dwarf accretion disk. The He I absorption feature is complex, extending to -2100 km/s with other discrete absorption components near -1750, -1500, -1000, and -650 km/s. The H I transitions display P Cygni absorption profiles with a similar negative velocity to the He I 1.083 micron feature. We estimate 10-10 solar masses for the jet along the line of sight towards MWC 560. We use line ratios to infer densities and emission mechanisms.