  We present measurements of the power spectra of cosmic infrared background
(CIB) and cosmic microwave background (CMB) fluctuations in six frequency
bands. Maps at the lower three frequency bands, 95, 150, and 220 GHz (3330,
2000, 1360 $\mu$m) are from the South Pole Telescope, while the upper three
frequency bands, 600, 857, and 1200 GHz (500, 350, 250 $\mu$m) are observed
with Herschel/SPIRE. From these data, we produce 21 angular power spectra (six
auto- and fifteen cross-frequency) spanning the multipole range $600 \le \ell
\le 11,000$. Our measurements are the first to cross-correlate measurements
near the peak of the CIB spectrum with maps at 95 GHz, complementing and
extending the measurements from Planck Collaboration et al. (2014) at 218, 550,
and 857 GHz. The observed fluctuations originate largely from clustered,
infrared-emitting, dusty star-forming galaxies, the CMB, and to a lesser extent
radio galaxies, active galactic nuclei, and the Sunyaev-Zel'dovich effect.
