CN / TiCN / TiN multilayers and the respective single layers have been deposited on Si͑100͒ substrates using a dual ion-beam sputtering system. Both the multilayers and the respective single layers have been chemically characterized by Auger electron spectroscopy ͑AES͒ depth profiling combined with factor analysis and by Rutherford backscattering spectrometry ͑RBS͒. The combination of AES and RBS allows a quantitative chemical characterization of the multilayer and the respective single layers. Whereas RBS has some difficulties to determine the in-depth distribution of the light elements along the multilayer, AES depth profiling enables their quantitative analysis and even their chemical state along the multilayer. On the contrary, RBS shows its advantages to determine the heavy elements, including the contaminants incorporated during the deposition process ͑e.g., W͒. Under special experimental conditions it is shown that RBS is able to determine the composition of the single layers ͑i.e., CN / Si, TiCN / Si, and TiN / Si͒ in good agreement with AES depth profiling. As a result of this complementary use we obtain a complete quantitative chemical characterization of the single layers and multilayers. In addition, the thermal stability of the multilayers upon heating for 1 h in vacuum and ambient atmospheres at 500°C has been studied by AES depth profiling. The results show that whereas the multilayer is stable in vacuum it undergoes significant changes when it is heated in air. In fact, it is shown that annealing in air for 1 h causes the disappearance of the CN top layer and the oxidation of the TiCN layer that leads to the formation of TiO 2 on its surface.