The use of color in QR codes brings extra data capacity, but also inflicts tremendous challenges on the decoding process due to chromatic distortion, cross-channel color interference and illumination variation. Particularly, we further discover a new type of chromatic distortion in high-density color QR codes, cross-module color interference, caused by the high density which also makes the geometric distortion correction more challenging. To address these problems, we propose two approaches, namely, LSVM-CMI and QDA-CMI, which jointly model these different types of chromatic distortion. Extended from SVM and QDA, respectively, both LSVM-CMI and QDA-CMI optimize over a particular objective function to learn a color classifier. Furthermore, a robust geometric transformation method is proposed to accurately correct the geometric distortion for high-density color QR codes. We put forth and implement a framework for high-capacity color QR codes equipped with our methods, called HiQ. To evaluate the performance of HiQ, we collect a challenging large-scale color QR code dataset, CUHK-CQRC, which consists of 5390 high-density color QR code samples. The comparison with the baseline method  on CUHK-CQRC shows that HiQ at least outperforms  by 188% in decoding success rate and 60% in bit error rate. Our implementation of HiQ in iOS and Android also demonstrates the effectiveness of our framework in real-world applications.