The 'Internal Linear Combination' (ILC) component separation method has been extensively used to extract a single component, the cosmic microwave background (CMB), from the WMAP multifrequency data. We generalize the ILC approach for separating other millimetre astrophysical emissions. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalized ILC methods, implemented on a needlet frame, is tested on simulations of Planck mission observations, for which we successfully reconstruct a low-noise estimate of emission from astrophysical foregrounds with vanishing CMB and Sunyaev-Zel'dovich contamination.