The emergence of multiparametric diffusion models combining diffusion and relaxometry measurements provides powerful new ways to explore tissue microstructure, with the potential to provide new insights into tissue structure and function. However, their ability to provide rich analyses and the potential for clinical translation critically depends on the availability of efficient, integrated, multi-dimensional acquisitions. We propose a fully integrated sequence simultaneously sampling the acquisition parameter spaces required for T1 and T2* relaxometry and diffusion MRI. Slice-level interleaved diffusion encoding, multiple spin/gradient echoes and slice-shuffling are combined for higher efficiency, sampling flexibility and enhanced internal consistency. In-vivo data was successfully acquired on healthy adult brains. Obtained parametric maps as well as clustering results demonstrate the potential of the technique to provide eloquent data with an acceleration of roughly 20 compared to conventionally used approaches. The proposed integrated acquisition, which we call ZEBRA, offers significant acceleration and flexibility compared to existing diffusion-relaxometry studies, and thus facilitates wider use of these techniques both for research-driven and clinical applications.