In the biomedical field, current technology allows for the collection of multiple data modalities from the same subject. In consequence, there is an increasing interest for methods to analyze multi-modal data sets. Methods based on independent component analysis have proven to be effective in jointly analyzing multiple modalities, including brain imaging and genetic data. This paper describes a new algorithm, three-way parallel independent component analysis (3pICA), for jointly identifying genomic loci associated with brain function and structure. The proposed algorithm relies on the use of multi-objective optimization methods to identify correlations among the modalities and maximally independent sources within modality. We test the robustness of the proposed approach by varying the effect size, cross-modality correlation, noise level, and dimensionality of the data. Simulation results suggest that 3p-ICA is robust to data with SNR levels from 0 to 10 dB and effect-sizes from 0 to 3, while presenting its best performance with high cross-modality correlations, and more than one subject per 1,000 variables. In an experimental study with 112 human subjects, the method identified links between a genetic component (pointing to brain function and mental disorder associated genes, including PPP3CC, KCNQ5, and CYP7B1), a functional component related to signal decreases in the default mode network during the task, and a brain structure component indicating increases of gray matter in brain regions of the default mode region. Although such findings need further replication, the simulation and in-vivo results validate the three-way parallel ICA algorithm presented here as a useful tool in biomedical data decomposition applications.