Motivation: Modelling methods that find structure in data are necessary with the current large volumes of genomic data, and there have been various efforts to find subsets of genes exhibiting consistent patterns over subsets of treatments. These biclustering techniques have focused on one data source, often gene expression data. We present a Bayesian approach for joint biclustering of multiple data sources, extending a recent method Group Factor Analysis to have a biclustering interpretation with additional sparsity assumptions. The resulting method enables data-driven detection of linear structure present in parts of the data sources. Results: Our simulation studies show that the proposed method reliably infers biclusters from heterogeneous data sources. We tested the method on data from the NCI-DREAM drug sensitivity prediction challenge, resulting in an excellent prediction accuracy. Moreover, the predictions are based on several biclusters which provide insight into the data sources, in this case on gene expression, DNA methylation, protein abundance, exome sequence, functional connectivity fingerprints and drug sensitivity.