We report resolved near-infrared spectroscopic monitoring of the nearby L dwarf/T dwarf binary WISE J104915.57-531906.1 AB (Luhman 16AB), as part of a broader campaign to characterize the spectral energy distribution and temporal variability of this system. A continuous 45 minute sequence of low-resolution IRTF/SpeX data spanning 0.8-2.4 mu m were obtained, concurrent with combined-light optical photometry with ESO/ TRAPPIST. We estimate a peak-to-peak amplitude of 13.5% at 1.25 mu m over the full light curve. Using a simple two-spot brightness temperature model for Luhman 16B, we infer an average cold covering fraction of approximately 30%-55%, varying by 15%-30% over a rotation period assuming a approximately 200-400 K difference between hot and cold regions. The strong variability observed in this flux reversal brown dwarf pair supports the model of a patchy disruption of the mineral cloud layer as a universal feature of the L dwarf/T dwarf transition.