This article presents the efficient mixed model analysis, often called global–local approach, to obtain interlaminar stresses at free edges in the laminated composite system under extension and flexure. For the proposed analysis, first, the discrete-layer elements are adopted as three-dimensional elements in the local region. Second, the equivalent single-layer elements are considered as two-dimensional elements in the global region. Finally, the mixed-dimensional transition elements are formulated to connect two different element types used in the global as well as the local regions, respectively. All the elements have higher order shape functions derived from the Lobatto shape function. Modes of the elements are classified into nodal and nodeless modes. The nodal modes have physical meaning, while nodeless modes with respect to the increase of order of the Lobatto shape function do not have physical meaning but improve accuracy of analysis. Therefore, fixing mesh arrangement of present analysis, the quality of the analysis can be enhanced without remeshing work. Some results obtained by the proposed approach are verified with comparison with published references. Also, efficiency of the mixed model analysis using the mixed-dimensional transition element is shown through comparison with numerical results obtained by the single model analysis using only discrete-layer elements.