We describe a framework for creating a time-resolved group average template of the developing brain using advanced multi-shell high angular resolution diffusion imaging data, for use in group voxel or fixel-wise analysis, atlas-building, and related applications. This relies on the recently proposed multi-shell multi-tissue constrained spherical deconvolution (MSMT-CSD) technique. We decompose the signal into one isotropic component and two anisotropic components, with response functions estimated from cerebrospinal fluid and white matter in the youngest and oldest participant groups, respectively. We build an orientationally-resolved template of those tissue components from data acquired from 113 babies between 33 and 44 weeks postmenstrual age, imaged as part of the Developing Human Connectome Project. These data were split into weekly groups, and registered to the corresponding group average templates using a previously-proposed non-linear diffeomorphic registration framework, designed to align orientation density functions (ODF). This framework was extended to allow the use of the multiple contrasts provided by the multi-tissue decomposition, and shown to provide superior alignment. Finally, the weekly templates were registered to the same common template to facilitate investigations into the evolution of the different components as a function of age. The resulting multi-tissue atlas provides insights into brain development and accompanying changes in microstructure, and forms the basis for future longitudinal investigations into healthy and pathological white matter maturation.