We have obtained the first high spatial (0.05) and spectral (R~35000) resolution 2 micron spectrum of the T Tau S tight binary system using adaptive optics on the Keck II telescope. We have also obtained the first 3.8 and 4.7 micron images that resolve the three components of the T Tau multiple system, as well as new 1.6 and 2.2 micron images. Together with its very red near-infrared colors, the spectrum of T Tau Sb shows that this T Tauri star is extincted by a roughly constant extinction of Av~15 mag, which is probably the 0.7x0.5 circumbinary structure recently observed in absorption in the ultraviolet. T Tau Sa, which is also observed through this screen and is actively accreting, further possesses a small edge-on disk that is evidenced by warm (390 K), narrow overtone CO rovibrational absorption features in our spectrum. We find that T Tau Sa is most likely an intermediate-mass star surrounded by a semi-transparent 2-3 AU-radius disk whose asymmetries and short Keplerian rotation explain the large photometric variability of the source on relatively short timescales. We also show that molecular hydrogen emission exclusively arises from the gas that surrounds T Tau S and that its spatial and kinematic structure, while providing suggestive evidence for a jet-like structure, is highly complex.