Accurate prediction of time-to-event outcomes, commonly known as survival analysis, is vital in high-stakes domains such as healthcare and business, where timely and trustworthy insights can have profound implications. Traditional survival analysis methods either provide predictions without clear explanations or offer interpretability without a mechanism to integrate expert insights. In many real-world scenarios, decision-makers require models that are both transparent and capable of interactively incorporating domain knowledge to refine predictions. The key challenge we address is how to simultaneously achieve accurate time-to-event forecasting, clear interpretability, and interactive integration of expert feedback. We propose the Interpretable and Interactive Deep Discrete-Time Survival Analysis framework, an approach that is both data-driven and knowledge-driven. Furthermore, it embeds expert knowledge into the model, dynamically aligns feature contributions with evolving risk patterns, and actively engages experts to guide the learning process interactively. This interactive strategy not only enhances predictive performance but also produces explanations that clearly reflect the critical factors identified by domain experts. Extensive evaluations on diverse clinical and business datasets demonstrate that our method captures feature importance and yields robust and reliable predictions that stand in contrast to conventional black-box models. These results indicate that bridging interpretability with interactive expert engagement can significantly improve decision support systems. By integrating accurate forecasting with human-aligned, interactive explanations, our framework offers a promising direction for developing more transparent and trusted models across a wide range of disciplines.