Interference, where the superposition of two or more waves resulting in a new wave pattern, has been considered as one of the most important and fundamental physical phenomenon. In optics, the statistical properties of light play an important role in determining the outcome of most optical experiments and the cross correlation between the fluctuating fields at different space time points, known as the optical coherence functions, is a quantity of great interest. Due to the fact that the wave equations govern propagation of optical coherence, it can be envisaged that the interference phenomena also appear in the format of the optical coherence function. Meanwhile, the study of propagation and superposition of optical coherence function also provides theoretical and experimental foundations for coherence holography. In this paper, we have given the mathematical expression of interference of the optical coherence functions, and have proposed a full-field coherence visualization system for coherence holographic interferometry. The interference of two optical coherence functions has been experimentally investigated which can be regarded as an extension of Young’s double-slit interferometer for optical waves. Some interesting phenomena, such as missing class of the coherence function and multiple-coherence function interference are demonstrated for the first time.