Advances in technology have enabled generation of multiple types of -omics data in many biomedical and clinical studies, and it is desirable to pool such data in order to improve the power of identifying important molecular signatures and patterns. However, such integrative analyses present new analytical and computational challenges. To address some of these challenges, we propose a Bayesian sparse generalized biclustering analysis (GBC) which enables integrating multiple omics modalities with incorporation of biological knowledge through the use of adaptive structured shrinkage priors. The proposed methods can accommodate both continuous and discrete data. MCMC and EM algorithms are developed for estimation. Numerical studies are conducted to demonstrate that our methods achieve improved feature selection and prediction in identifying disease subtypes and latent drivers, compared to existing methods.