A series of sputtered as-prepared and annealed Ge/C multilayer structures with periods ranging from 2 to 8 nm has been studied with high resolution transmission electron microscopy (HRTEM), x-ray scattering, and stress measurement techniques. Ge/C multilayers have potential applications as normal incidence reflective mirrors near 4.4 nm wavelength. The reflectivity and stress in these structures depend on the microstructural evolution of the component layers. The as-prepared structure of both Ge and C layers appear amorphous from TEM imaging and diffraction. Annealing at 500°C for 60 minutes leads to crystallization of the Ge layers. As the phase diagram indicates, no carbide compound has been found. X-ray scattering reveals that the multilayer period expands by as much as 10% after annealing. Both TEM images and x-ray profiles suggest that the layer structures remain well-defined upon annealing. In-situ stress-temperature measurements directly show the Ge/C multilayer microstructure evolution path. X-ray measurements show that the structures with periods near 2 nm undergo a significant improvement on optical performance with annealing. The physical mechanisms that may have caused the optical enhancement are discussed. Correlation of the stress evolution in the multilayers and in individual layers during annealing, and their relationships to the microstructures and optical properties are examined.