Electromagnetic relays (EMRs) are intricate micro-electromechanical systems characterized by nonlinear behavior and coupling effects between electromagnetic and mechanical forces. Accurately modeling degradation and assessing reliability are crucial yet challenging tasks for ensuring their safe and efficient operation. Current data-driven methods for degradation modeling and reliability assessment often neglect the known physical knowledge regarding EMRs, leading to inaccuracies in modeling and assessment outcomes when data is incomplete. While physics-informed machine learning (PIML) approaches offer a potential solution, common regression models like Gaussian processes (GP) and long short-term memory (LSTM) suffer from underfitting and overfitting, respectively. To address these issues, we presents a hybrid PIML approach for time-dependent reliability assessment based on the emerging variational autoencoder (VAE) framework. This approach combines the advantages of GP-based methods that enable probabilistic representation with deep neural network-based methods that are more flexible and computationally efficient. Finally, we validate our proposed approach using real-world engineering data, demonstrating its superior accuracy and computational efficiency compared to state-of-the-art methods.