Among the most prevalent motion planning techniques, sampling and trajectory optimization have emerged successful due to their ability to handle tight constraints and high-dimensional systems, respectively. However, limitations in sampling in higher dimensions and local minima issues in optimization have hindered their ability to excel beyond static scenes in offline settings. Here we consider highly dynamic environments with long horizons that necessitate a fast online solution. We present a unified approach that leverages the complementary strengths of sampling and optimization, and interleaves them both in a manner that is well suited to this challenging problem. With benchmarks in multiple synthetic and realistic simulated environments, we show that our approach performs significantly better on various metrics against baselines that employ either only sampling or only optimization. Project page: https://sites.google.com/view/jistplanner