We present a new formulation for the multilayer Isogeometric Kirchhoff--Love (KL) shells, where the individual layers are assumed to interact through no-penetration and frictional contact. This work is largely motivated by the experiments and analysis presented in . We utilize a regularized version of Coulomb's friction law to model the tangential traction between the contacting shell surfaces. To ensure objectivity (i.e., reference-frame invariance) in the frictional model, we propose two different strategies to extrapolate the velocity vectors of the contact pair at the contact interface: (i) Using the underlying KL kinematics of the individual shell layers and (ii) Using the Taylor series-based extension from . We compare the performance of both approaches through a numerical benchmark example. We then validate our multilayer shell formulation using the ‘bending response of a book with internal friction’ experiments of .