Structures that emerge at stratified mesoscales in complex networks affect the collective behavior of nodes. Simplicial complexes are convenient as they present a convenient foundation to study this behavior, due to their rich aggregation properties. The presented research proposes extending the homological approach for comparing topological objects to include higher-order layered aggregations of connected structures. Pursuing this goal, the similarity criterion between two simplicial complexes is derived based on the properties of the spectra of higher-order combinatorial Laplacian. The calculations are performed for a suitable example and compared with another similarity criterion between simplicial complexes, in which mesoscale simplicial connectivities are implicitly included. The results suggest that the proposed criterion can strengthen the homological approach and have broad practical applications, particularly since different simplicial complexes can be formed from a network.