The infinite order sudden (IOS) treatment of the dynamics that yields the necessary collision integrals for the calculation of transport coefficients is tested for a gaseous mixture that includes a nonlinear polyatomic partner, the methane molecule, interacting with He. The use of a fully anisotropic potential obtained before from crossed beam experiments is shown to provide rather good agreement with the available experiments for diffusion and viscosity coefficients over a broad range of temperatures. The comparison with more accurate calculations already carried out by us also shows extremely good agreement between the IOS calculations and the earlier, much more costly, evaluation through a quantum coupled states dynamics. The present calculations therefore indicate that, even for a more complicated nonlinear molecular partner in the mixture, IOS results for diffusion and viscosity coefficients can provide a way of further improving the chosen form for the full potential energy surface of the system.