Metric Learning for visual similarity has mostly adopted binary supervision indicating whether a pair of images are of the same class or not. Such a binary indicator covers only a limited subset of image relations, and is not sufficient to represent semantic similarity between images described by continuous and/or structured labels such as object poses, image captions, and scene graphs. Motivated by this, we present a novel method for deep metric learning using continuous labels. First, we propose a new triplet loss that allows distance ratios in the label space to be preserved in the learned metric space. The proposed loss thus enables our model to learn the degree of similarity rather than just the order. Furthermore, we design a triplet mining strategy adapted to metric learning with continuous labels. We address three different image retrieval tasks with continuous labels in terms of human poses, room layouts and image captions, and demonstrate the superior performance of our approach compared to previous methods.