  We consider the rigorously derived thin shell membrane $\Gamma$-limit of a
three-dimensional isotropic geometrically nonlinear Cosserat micropolar model
and deduce full interior regularity of both the midsurface deformation
$m:\omega\subset{\mathbb R}^2\to{\mathbb R}^3$ and the orthogonal microrotation
tensor field $R:\omega\subset{\mathbb R}^2\to SO(3)$. The only further
structural assumption is that the curvature energy depends solely on the
uni-constant isotropic Dirichlet type energy term $|DR|^2$. We use Rivi\`ere's
regularity techniques of harmonic map type systems for our system which couples
harmonic maps to $SO(3)$ with a linear equation for $m$. The additional
coupling term in the harmonic map equation is of critical integrability and can
only be handled because of its special structure.
