We investigate hybrid user interfaces (HUIs), aiming to establish a cohesive understanding and to adopt consistent terminology for this nascent research area. HUIs combine heterogeneous devices in complementary roles, leveraging the distinct benefits of each. Our work focuses on cross-device interaction between 2D devices and mixed reality environments, which are particularly compelling, leveraging the familiarity of traditional 2D platforms while providing spatial awareness and immersion. Although prior work has prominently explored such HUIs in the context of mixed reality, we still lack a cohesive understanding of the unique design possibilities and challenges of such combinations, resulting in a fragmented research landscape. We conducted a systematic survey and present a taxonomy of HUIs that combine conventional display technology and mixed reality environments. Based on this, we discuss past and current challenges, the evolution of definitions, and prospective opportunities to tie together the past 30 years of research with our vision of future HUIs.