Image quality assessment (IQA) for authentic distortions in the wild is challenging. Though current IQA metrics have achieved decent performance for synthetic distortions, they still cannot be satisfactorily applied to realistic distortions because of the generalization problem. Improving generalization ability is an urgent task to make IQA algorithms serviceable in real-world applications, while relevant research is still rare. Fundamentally, image quality is determined by both distortion degree and intelligibility. However, current IQA metrics mostly focus on the distortion aspect and do not fully investigate the intelligibility, which is crucial for achieving robust quality estimation. Motivated by this, this paper presents a new framework for building highly generalizable image quality model by integrating the intelligibility. We first analyze the relation between intelligibility and image quality. Then we propose a bilateral network to integrate the above two aspects of image quality. During the fusion process, feature selection strategy is further devised to avoid negative transfer. The framework not only catches the conventional distortion features but also integrates intelligibility features properly, based on which a highly generalizable no-reference image quality model is achieved. Extensive experiments are conducted based on five intelligibility tasks, and the results demonstrate that the proposed approach outperforms the state-of-the-art metrics, and the intelligibility task consistently improves metric performance and generalization ability.