We propose a novel deep neural network architecture to integrate imaging and genetics data, as guided by diagnosis, that provides interpretable biomarkers. Our model consists of an encoder, a decoder and a classifier. The encoder learns a non-linear subspace shared between the input data modalities. The classifier and the decoder act as regularizers to ensure that the low-dimensional encoding captures predictive differences between patients and controls. We use a learnable dropout layer to extract interpretable biomarkers from the data, and our unique training strategy can easily accommodate missing data modalities across subjects. We have evaluated our model on a population study of schizophrenia that includes two functional MRI (fMRI) paradigms and Single Nucleotide Polymorphism (SNP) data. Using 10-fold cross validation, we demonstrate that our model achieves better classification accuracy than baseline methods, and that this performance generalizes to a second dataset collected at a different site. In an exploratory analysis we further show that the biomarkers identified by our model are closely associated with the well-documented deficits in schizophrenia.