Ethane core-silver shell clusters consisting of several thousand particles have been assembled in helium droplets upon capture of ethane molecules followed by Ag atoms. The composite clusters were studied via infrared laser spectroscopy in the range of the C-H stretching vibrations of ethane. The spectra reveal a splitting of the vibrational bands, which is ascribed to interaction with Ag. A rigorous analysis of band intensities for a varying number of trapped ethane molecules and Ag atoms indicates that the composite clusters consist of a core of ethane that is covered by relatively small Ag clusters. This metastable structure is stabilized due to fast dissipation in superfluid helium droplets of the cohesion energy of the clusters.