We map the distribution and properties of the Milky Way's interstellar medium as traced by diffuse interstellar bands (DIBs) detected in near-infrared stellar spectra from the SDSS-III/APOGEE survey. Focusing exclusively on the strongest DIB in the H-band, at ~1.527 microns, we present a projected map of the DIB absorption field in the Galactic plane, using a set of about 60,000 sightlines that reach up to 15 kpc from the Sun and probe up to 30 magnitudes of visual extinction. The strength of

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... is DIB is linearly correlated with dust reddening over three orders of magnitude in both DIB equivalent width (W_DIB) and extinction, with a power law index of 1.01 +/- 0.01, a mean relationship of W_DIB/A_V = 0.1 Angstrom mag^-1, and a dispersion of ~0.05 Angstrom mag^-1 at extinctions characteristic of the Galactic midplane. These properties establish this DIB as a powerful, independent probe of dust extinction over a wide range of A_V values. The subset of about 14,000 robustly detected DIB features have an exponential W_DIB distribution. We empirically determine the intrinsic rest wavelength of this transition to be lambda_0 = 15,272.42 Angstrom, and then calculate absolute radial velocities of the carrier, which display the kinematical signature of the rotating Galactic disk. We probe the DIB carrier distribution in three dimensions and show that it can be characterized by an exponential disk model with a scaleheight of about 100 pc and a scalelength of about 5 kpc. Finally, we show that the DIB distribution also traces large-scale Galactic structures, including the central long bar and the warp of the outer disk.