The 'Internal Linear Combination' (ILC) component separation method has been extensively used on the data of the Wilkinson Microwave Anisotropy Probe (WMAP) space mission, to extract a single component, the cosmic microwave background (CMB), from the WMAP multifrequency data. We extend the ILC approach for reconstructing millimetre astrophysical emissions beyond the CMB alone. In particular, we construct a constrained ILC to extract maps of both the CMB and the thermal Sunyaev-Zeldovich (SZ) effect, with vanishing contamination from the other. The performance of the constrained ILC is tested on simulations of Planck mission observations, for which we successfully reconstruct independent estimates of the CMB and of the thermal SZ.