This paper introduces a novel proprioceptive state estimator for legged robots that combines model-based filters with deep neural networks. In environments where vision systems are not reliable, proprioceptive state estimators become indispensable. Traditionally, proprioceptive state estimators are based on model-based approaches, which rely solely on contact foot kinematics as measurements. In contrast, learning-based approaches have obtained new measurements, such as displacement and covariance, by leveraging real-world data in a supervised manner. In this work, we develop a state estimation framework that trains a neural measurement network (NMN) to estimate the base's linear velocity and foot contact probability, which are then employed as measurements in an invariant extended Kalman filter. Our approach relies solely on simulation data for training, as it allows us to obtain extensive data easily. We address the sim-to-real gap by adapting existing learning techniques and regularization. To validate our proposed method, we conduct hardware experiments using a quadruped robot on four types of terrain: flat, debris, soft, and slippery. In our experiments, the proposed method demonstrates significant improvements over the model-based state estimator, achieving an average reduction in Absolute Trajectory Error (ATE) by 61.8% for position and 8.5% for velocity.