Human face captured at night or in dimly lit environments has become a common practice, accompanied by complex low-light and low-resolution degradations. However, the existing face super-resolution (FSR) technologies and derived cascaded schemes are inadequate to recover credible textures. In this paper, we propose a novel approach that decomposes the restoration task into face structural fidelity maintaining and texture consistency learning. The former aims to enhance the quality of face images while improving the structural fidelity, while the latter focuses on eliminating perturbations and artifacts caused by low-light degradation and reconstruction. Based on this, we develop a novel low-light low-resolution face super-resolution framework. Our method consists of two steps: an illumination correction face super-resolution network (IC-FSRNet) for lighting the face and recovering the structural information, and a detail enhancement model (DENet) for improving facial details, thus making them more visually appealing and easier to analyze. As the relighted regions could provide complementary information to boost face super-resolution and vice versa, we introduce the mutual learning to harness the informative components from relighted regions and reconstruction, and achieve the iterative refinement. In addition, DENet equipped with diffusion probabilistic model is built to further improve face image visual quality. Experiments demonstrate that the proposed joint optimization framework achieves significant improvements in reconstruction quality and perceptual quality over existing two-stage sequential solutions. Code is available at https://github.com/wcy-cs/IC-FSRDENet.