The intricacy of rainy image contents often leads cutting-edge deraining models to image degradation including remnant rain, wrongly-removed details, and distorted appearance. Such degradation is further exacerbated when applying the models trained on synthetic data to real-world rainy images. We raise an intriguing question -- if leveraging both accessible unpaired clean/rainy yet real-world images and additional detail repair guidance, can improve the generalization ability of a deraining model? To answer it, we propose a semi-supervised detail-recovery image deraining network (termed as Semi-DRDNet). Semi-DRDNet consists of three branches: 1) for removing rain streaks without remnants, we present a \textit{squeeze-and-excitation} (SE)-based rain residual network; 2) for encouraging the lost details to return, we construct a \textit{structure detail context aggregation} (SDCAB)-based detail repair network; to our knowledge, this is the first time; and 3) for bridging the domain gap, we develop a novel contrastive regularization network to learn from unpaired positive (clean) and negative (rainy) yet real-world images. As a semi-supervised learning paradigm, Semi-DRDNet operates smoothly on both synthetic and real-world rainy data in terms of deraining robustness and detail accuracy. Comparisons on four datasets show clear visual and numerical improvements of our Semi-DRDNet over thirteen state-of-the-arts.