In this paper, we present a class of mixed-reality displays which allow for the 3D exploration of content in public exhibitions. The shared experience of the exhibition and the preservation of artworks are two very important aspects of these contexts, in particular for museum exhibits. The use of display cases as a protection tool is substantially accepted. It decreases the risks of damages to artworks and cultural materials hosted in museums. In addition, the transparent panels create a reflection of the visitors inside the display case. This reflection can be used to augment and interact in 3D with the exhibited content, by coupling Spatial Augmented-Reality and Optical Combiners. We call such a combination a Revealable Volume Display (RVD). It allows visitors to reveal information placed freely inside or around protected artefacts, visible by all, using their reflection in the panel. However, it may also suffer from unfamiliar gestures and disrupted depth perception cues, making 3D exploration of content difficult. In this paper, we first discuss the implementation of RVDs, providing both projector-based and mobile versions. We then present a design space that describes the interaction possibilities that they offer. Drawing on insights from a field study during a first exhibition, we finally propose and evaluate techniques for facilitating 3D exploration with RVDs.