Despite the significant progress of deep learning models in multitude of applications, their adaption in planning and policy related areas remains challenging due to the black-box nature of these models. In this work, we develop a set of DeepLogit models that follow a novel sequentially constrained approach in estimating deep learning models for transport policy analysis. In the first step of the proposed approach, we estimate a convolutional neural network (CNN) model with only linear terms, which is equivalent of a linear-in-parameter multinomial logit model. We then estimate other deep learning models by constraining the parameters that need interpretability at the values obtained in the linear-in-parameter CNN model and including higher order terms or by introducing advanced deep learning architectures like Transformers. Our approach can retain the interpretability of the selected parameters, yet provides significantly improved model accuracy than the discrete choice model. We demonstrate our approach on a transit route choice example using real-world transit smart card data from Singapore. This study shows the potential for a unifying approach, where theory-based discrete choice model (DCM) and data-driven AI models can leverage each other's strengths in interpretability and predictive power. With the availability of larger datasets and more complex constructions, such approach can lead to more accurate models using discrete choice models while maintaining its applicability in planning and policy-related areas. Our code is available on https://github.com/jeremyoon/route-choice/ .