The absorption shapes of the ν 2, ν 3 and ν 4 infrared bands of CH 4 perturbed by H 2 in large ranges of pressure and temperature have been measured in the laboratory. In order to model these spectra, the theoretical approach accounting for line-mixing effects proposed for CH 4–N 2 and CH 4-air and successfully tested in the companion paper (I), is used. As before, state-to-state rotational rates are used together with some empirical parameters that are deduced from a fit of a single room temperature spectrum of the ν 3 band at about 50 atm. The comparisons between measured and calculated spectra in the ν 3 and ν 4 regions under a vast variety of conditions (9–300 atm, 80–300 K) then demonstrate the quality and consistency of the proposed model. In the case of the ν 2 band, which is of E symmetry, specific parameters, different from those adapted to the ν 3 and ν 4 transitions of F 2 symmetry, are used for proper modeling of the spectral shape. Furthermore, as shown previously, a broad absorption feature grows underneath the ν 2 band with increasing H 2 density. The latter, for which an empirical model is proposed, is attributed to a collision-induced absorption (CIA) process in methane. From the developed models, a database and associated software are built for the updating of planetary atmospheres radiative transfer codes. The quality of these tools is then further demonstrated using emission measurements of the Jovian and Saturnian atmospheres in the ν 4 region (7–10 μm) recorded by the Short Wave Spectrometer of the Infrared Space Observatory and the Composite Infrared Spectrometer on-board Cassini. Comparisons between measured radiances and predictions confirm the failure of the purely Lorentzian approach and the quality of the proposed line-mixing model. Furthermore, it is shown that the methane CIA contribution has a significant influence on the planetary emission beyond 1400 cm −1.