  We investigate the cross-correlation between the cosmic infrared and
microwave backgrounds (CIB & CMB) anisotropies through the integrated
Sachs-Wolfe effect. We first describe the CIB anisotropies using a linearly
biased power spectrum, then derive the theoretical angular power spectrum of
the CMB-CIB cross-correlation for different instruments and frequencies. We
discuss the detectability of the ISW signal by performing a signal-to-noise
(SNR) analysis with our predicted spectra. The significances obtained range
from 6{\sigma} to 7{\sigma} in an ideal case, depending on the frequency ; in
realistic cases which account for the presence of noise including astrophysical
contaminants, the results span the range 2-5{\sigma}, depending strongly on the
major contribution to the noise term.
