Building upon recent works devoted to the development of a stress-based layerwise model for multilayered plates, we explore an alternative finite-element discretization to the conventional displacement-based finite-element method. We rely on a mixed finite-element approach where both stresses and displacements are interpolated. Since conforming stress-based finite-elements ensuring traction continuity are difficult to construct, we consider a hybridization strategy in which traction continuity is relaxed by the introduction of an additional displacement-like Lagrange multiplier defined on the element facets. Such a strategy offers the advantage of uncoupling many degrees of freedom so that static condensation can be performed at the element level, yielding a much smaller final system to solve. Illustrative applications demonstrate that the proposed mixed approach is free from any shear-locking in the thin plate limit and is more accurate than a displacement approach for the same number of degrees of freedom. As a result, this method can be used to capture efficiently strong intra- and inter-laminar stress variations near free-edges or cracks.