We present GDLNN, a new graph machine learning architecture, for graph classification tasks. GDLNN combines a domain-specific programming language, called GDL, with neural networks. The main strength of GDLNN lies in its GDL layer, which generates expressive and interpretable graph representations. Since the graph representation is interpretable, existing model explanation techniques can be directly applied to explain GDLNN's predictions. Our evaluation shows that the GDL-based representation achieves high accuracy on most graph classification benchmark datasets, outperforming dominant graph learning methods such as GNNs. Applying an existing model explanation technique also yields high-quality explanations of GDLNN's predictions. Furthermore, the cost of GDLNN is low when the explanation cost is included.