In the integrative analyses of omics data, it is often of interest to extract data representation from one data type that best reflect its relations with another data type. This task is traditionally fulfilled by linear methods such as canonical correlation analysis (CCA) and partial least squares (PLS). However, information contained in one data type pertaining to the other data type may be complex and in nonlinear form. Deep learning provides a convenient alternative to extract low-dimensional nonlinear data embedding. In addition, the deep learning setup can naturally incorporate the effects of clinical confounding factors into the integrative analysis. Here we report a deep learning setup, named Autoencoder-based Integrative Multi-omics data Embedding (AIME), to extract data representation for omics data integrative analysis. The method can adjust for confounder variables, achieve informative data embedding, rank features in terms of their contributions, and find pairs of features from the two data types that are related to each other through the data embedding. In simulation studies, the method was highly effective in the extraction of major contributing features between data types. Using two real microRNA-gene expression datasets, one with confounder variables and one without, we show that AIME excluded the influence of confounders, and extracted biologically plausible novel information. The R package based on Keras and the TensorFlow backend is available at https://github.com/tianwei-yu/AIME.