Coupling beams, shells, and solids in a single simulation is a key challenge in structural mechanics. Finite strain Cosserat elasticity provides a natural framework for this purpose, as it supports large deformations together with independent translational and rotational fields already in the bulk model. Many existing coupling strategies rely on special meshes or additional constraints. We propose a unified Cosserat formulation in which beam and shell models are obtained by kinematical reduction of the three-dimensional continuum, while preserving the same degrees of freedom and explicitly accounting for large initial geometric curvatures of curved beams and shells. The interaction between domains of different dimension is imposed through Sobolev trace operators, which results in a mixed-dimensional energy minimisation problem. This yields intrinsic compatibility at interfaces without auxiliary variables. We sketch the derivation of the mixed-dimensional models, demonstrate the approach with numerical examples, and conclude with an outlook on future work.