In this brief, we present a constant time method for the joint bilateral filtering. First, we propose an image data structure, coined as joint integral histograms (JIHs). Extending the classic integral images and the integral histograms, it represents the global information of two correlated images. In a JIH, the value at each bin indicates an integral determined by the two images. Then, the joint bilateral filtering is transformed to computation and manipulation of histograms. Utilizing the JIHs, we are capable of joint bilateral filtering in constant time. Its performance is validated in a digital photography approach using Flash-noFlash image pairs. Compared with the brute-force method, the proposed method achieves a speedup factor of 2-3 orders of magnitude while producing similar filtering results.