Structural similarity networks are a central focus of magnetic resonance imaging (MRI) research into human brain connectomes in health and disease. We present Morphometric INverse Divergence (MIND), a robust method to estimate within-subject structural similarity between cortical areas based on the Kullback-Leibler divergence between the multivariate distributions of their structural features. Compared to the prior approach of morphometric similarity networks (MSNs) on N>10,000 data from the ABCD cohort, MIND networks were more consistent with known cortical symmetry, cytoarchitecture, and (in N=19 macaques) gold-standard tract-tracing connectivity, and were more invariant to cortical parcellation. Importantly, MIND networks were remarkably coupled with cortical gene co-expression, providing fresh evidence for the unified architecture of brain structure and transcription. Using kinship (N=1282) and genetic data (N=4085), we characterized the heritability of MIND phenotypes, identifying stronger genetic influence on the relationship between structurally divergent regions compared to structurally similar regions. Overall, MIND presents a biologically-validated lens for analyzing the structural organization of the cortex using readily-available MRI measurements.