We use analytic computations to predict the power spectrum as well as the bispectrum of cosmic infrared background (CIB) anisotropies. Our approach is based on the halo model and takes into account the mean luminosity-mass relation. The model is used to forecast the possibility to simultaneously constrain cosmological, CIB, and halo occupation distribution (HOD) parameters in the presence of foregrounds. For the analysis, we use wavelengths in eight frequency channels between 200 and 900 GHz with survey specifications given by Planck and LiteBird. We explore the sensitivity to the model parameters up to multipoles of ι = 1000 using autocorrelation and cross-correlation between the different frequency bands. With this setting, cosmological, HOD, and CIB parameters can be constrained to a few per cent. Galactic dust is modelled by a power law and the shot-noise contribution as a frequency-dependent amplitude that are marginalized over. We find that dust residuals in the CIB maps only marginally influence constraints on standard cosmological parameters. Furthermore, the bispectrum yields tighter constraints (by a factor 4 in 1σ errors) on almost all model parameters, while the degeneracy directions are very similar to the ones of the power spectrum. The increase in sensitivity is most pronounced for the sum of the neutrino masses. Due to the similarity of degeneracies, a combination of both analysis is not needed for most parameters. This, however, might be due to the simplified bias description generally adopted in such halo model approaches.