MOTIVATION: Unsupervised clustering is important in disease subtyping, among having other genomic applications. As genomic data has become more multifaceted, how to cluster across data sources for more precise subtyping is an ever more important area of research. Many of the methods proposed so far, including iCluster and Cluster of Cluster Assignments (COCAs), make an unreasonable assumption of a common clustering across all data sources, and those that do not are fewer and tend to be computationally intensive. RESULTS: We propose a Bayesian parametric model for integrative, unsupervised clustering across data sources. In our two-way latent structure model, samples are clustered in relation to each specific data source, distinguishing it from methods like COCAs and iCluster, but cluster labels have across-dataset meaning, allowing cluster information to be shared between data sources. A common scaling across data sources is not required, and inference is obtained by a Gibbs Sampler, which we improve with a warm start strategy and modified density functions to robustify and speed convergence. Posterior interpretation allows for inference on common clusterings occurring among subsets of data sources. An interesting statistical formulation of the model results in sampling from closed-form posteriors despite incorporation of a complex latent structure. We fit the model with Gaussian and more general densities, which influences the degree of across-dataset cluster label sharing. Uniquely among integrative clustering models, our formulation makes no nestedness assumptions of samples across data sources so that a sample missing data from one genomic source can be clustered according to its existing data sources. We apply our model to a Norwegian breast cancer cohort of ductal carcinoma in situ and invasive tumors, comprised of somatic copy-number alteration, methylation and expression datasets. We find enrichment in the Her2 subtype and ductal carcinoma among those observations exhibiting greater cluster correspondence across expression and CNA data. In general, there are few pan-genomic clusterings, suggesting that models assuming a common clustering across genomic data sources might yield misleading results. AVAILABILITY AND IMPLEMENTATION: The model is implemented in an R package called twl ('two-way latent'), available on CRAN. Data for analysis are available within the R package. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.