In this paper, we examine the potential of incorporating transparent, handheld devices into head-mounted Augmented Reality (AR). Additional mobile devices have long been successfully used in head-mounted AR, but they obscure the visual context and real world objects during interaction. Transparent tangible displays can address this problem, using either transparent OLED screens or rendering by the head-mounted display itself. However, so far, there is no systematic analysis of the use of such transparent tablets in combination with AR head-mounted displays (HMDs), with respect to their benefits and arising challenges. We address this gap by introducing a research platform based on a touch-enabled, transparent interaction panel, for which we present our custom hardware design and software stack in detail. Furthermore, we developed a series of interaction concepts for this platform and demonstrate them in the context of three use case scenarios: the exploration of 3D volumetric data, collaborative visual data analysis, and the control of smart home appliances. We validate the feasibility of our concepts with interactive prototypes that we used to elicit feedback from HCI experts. As a result, we contribute to a better understanding of how transparent tablets can be integrated into future AR environments.