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Modern diffusion and functional magnetic resonance imaging (dMRI/fMRI) provide non-invasive high-resolution images from which multi-layered networks of whole-brain structural and functional connectivity can be derived. Unfortunately, the lack of observed correspondence between the connectivity profiles of the two modalities challenges the understanding of the relationship between the functional and structural connectome. Rather than focusing on correspondence at the level of connections we presently investigate correspondence in terms of modular organization according to shared canonical processing units. We use a stochastic block-model (SBM) as a data-driven approach for clustering high-resolution multi-layer whole-brain connectivity networks and use prediction to quantify the extent to which a given clustering accounts for the connectome within a modality. The employed SBM assumes a single underlying parcellation exists across modalities whilst permitting each modality to possess an independent connectivity structure between parcels thereby imposing concurrent functional and structural units but different structural and functional connectivity profiles. We contrast the joint processing units to their modality specific counterparts and find that even though data-driven structural and functional parcellations exhibit substantial differences, attributed to modality specific biases, the joint model is able to achieve a consensus representation that well accounts for both the functional and structural connectome providing improved representations of functional connectivity compared to using functional data alone. This implies that a representation persists in the consensus model that is shared by the individual modalities. We find additional support for this viewpoint when the anatomical correspondence between modalities is removed from the joint modeling. The resultant drop in predictive performance is in general substantial, confirming that the anatomical correspondence of processing units is indeed present between the two modalities. Our findings illustrate how multi-modal integration admits consensus representations well-characterizing each individual modality despite their biases and points to the importance of multi-layered connectomes as providing supplementary information regarding the brain's canonical processing units.