Amorphous CoMoN/CN compound soft-X-ray multilayers were fabricated by dual-facing-target sputtering. Their structural thermal stability has been investigated by monitoring the structural evolutions of CN and CoMoN sublayers at annealing temperatures up to 800 degreesC using complementary measurement techniques, and measuring the coefficient of interfacial diffusion at annealing temperatures below 300 degreesC. The period expansion at annealing temperatures below 600 degreesC, which is usually observed in annealed metal/carbon soft-X-ray multilayers, is only 5%. The enhanced sp(2) to sp(3) bond ratio caused by the "incorporation annealing effect" of nitrogen [1] is thought to be responsible for the improved thermal stability of CN sublayers. Mo addition greatly suppresses the structural thermal evolution of CoMoN sublayers. XPS and TEM analyses indicate that the strong chemical bonding between N and Co atoms and Mo nitride aggregation in the grain boundary of cobalt are the main mechanisms for the high thermal stability of CoMoN sublayers. The layered structure of the CoMoN/CN multilayers still exists at the annealing temperature of 800 degreesC, while Co/C and CoN/CN multilayers have already been destroyed at this temperature. Compared with Co/C and CoN/CN multilayers, the smaller negative interdiffusivity measured by X-ray diffraction reveals the stable interfaces of CoMoN/CN multilayers. These results illustrate that refractory metal incorporation and strong chemical bond establishment are quite effective in obtaining thermally highly stable compound soft-X-ray optical multilayers.