The structural characterization of heat-treated CN films fabricated by dual-facing-target sputtering for soft X-ray multilayer mirrors was performed by means of X-ray diffraction (XRD), Raman spectroscopy (RS) and X-ray photoelectron spectroscopy (XPS). The XRD analyses indicate a graphization process in the CN films during thermal annealing. The Raman analyses imply that the primary bonding in the CN films is sp2. In other words, the formation of the sp3 bonding in the CN films can be suppressed effectively by doping with N atoms, and thus the thickness expansion resulting from the changes in the density of CN films during annealing can be decreased considerably. This result is also clarified by the increased conductivity measured. The XPS results give the information of the existence of the strong covalent bonding between N and C atoms, which can slow down the tendency of the structural relaxation during annealing. These results suggest that CN films suitable for soft X-ray multilayers used at high-temperature environments can be obtained by reactive dual-facing-target sputtering. With the low-angle X-ray diffraction measurements, we do observe the enhanced thermal stability of CoN=CN multilayers.