Monumental advances in deep learning have led to unprecedented achievements across various domains. While the performance of deep neural networks is indubitable, the architectural design and interpretability of such models are nontrivial. Research has been introduced to automate the design of neural network architectures through neural architecture search (NAS). Recent progress has made these methods more pragmatic by exploiting distributed computation and novel optimization algorithms. However, there is little work in optimizing architectures for interpretability. To this end, we propose a multi-objective distributed NAS framework that optimizes for both task performance and "introspectability," a surrogate metric for aspects of interpretability. We leverage the non-dominated sorting genetic algorithm (NSGA-II) and explainable AI (XAI) techniques to reward architectures that can be better comprehended by domain experts. The framework is evaluated on several image classification datasets. We demonstrate that jointly optimizing for task error and introspectability leads to more disentangled and debuggable architectures that perform within tolerable error.