Studies have shown deep neural networks (DNN) as a potential tool for classifying dysarthric speakers and controls. However, representations used to train DNNs are largely not clinically interpretable, which limits clinical value. Here, a model with a bottleneck layer is trained to jointly learn a classification label and four clinically-interpretable features. Evaluation of two dysarthria subtypes shows that the proposed method can flexibly trade-off between improved classification accuracy and discovery of clinically-interpretable deficit patterns. The analysis using Shapley additive explanation shows the model learns a representation consistent with the disturbances that define the two dysarthria subtypes considered in this work.