Image super-resolution (SR) and image inpainting are two topical problems in medical image processing. Existing methods for solving the problems are either tailored to recovering a high-resolution version of the low-resolution image or focus on filling missing values, thus inevitably giving rise to poor performance when the acquisitions suffer from multiple degradations. In this paper, we explore the possibility of super-resolving and inpainting images to handle multiple degradations and therefore improve their usability. We construct a unified and scalable framework to overcome the drawbacks of propagated errors caused by independent learning. We additionally provide improvements over previously proposed super-resolution approaches by modeling image degradation directly from data observations rather than bicubic downsampling. To this end, we propose HLH-GAN, which includes a high-to-low (H-L) GAN together with a low-to-high (L-H) GAN in a cyclic pipeline for solving the medical image degradation problem. Our comparative evaluation demonstrates that the effectiveness of the proposed method on different brain MRI datasets. In addition, our method outperforms many existing super-resolution and inpainting approaches.