Recent studies compare gene expression data across species to identify core and species specific genes in biological systems. To perform such comparisons researchers need to match genes across species. This is a challenging task since the correct matches (orthologs) are not known for most genes. Previous work in this area used deterministic matchings or reduced multidimensional expression data to binary representation. Here we develop a new method that can utilize soft matches (given as priors) to infer both, unique and similar expression patterns across species and a matching for the genes in both species. Our method uses a Dirichlet process mixture model which includes a latent data matching variable. We present learning and inference algorithms based on variational methods for this model. Applying our method to immune response data we show that it can accurately identify common and unique response patterns by improving the matchings between human and mouse genes.