We investigate the use of image-and-spatial transformer networks (ISTNs) to tackle domain shift in multi-site medical imaging data. Commonly, domain adaptation (DA) is performed with little regard for explainability of the inter-domain transformation and is often conducted at the feature-level in the latent space. We employ ISTNs for DA at the image-level which constrains transformations to explainable appearance and shape changes. As proof-of-concept we demonstrate that ISTNs can be trained adversarially on a classification problem with simulated 2D data. For real-data validation, we construct two 3D brain MRI datasets from the Cam-CAN and UK Biobank studies to investigate domain shift due to acquisition and population differences. We show that age regression and sex classification models trained on ISTN output improve generalization when training on data from one and testing on the other site.