Our paper proposes a direct sparse visual odometry method that combines event and RGB-D data to estimate the pose of agile-legged robots during dynamic locomotion and acrobatic behaviors. Event cameras offer high temporal resolution and dynamic range, which can eliminate the issue of blurred RGB images during fast movements. This unique strength holds a potential for accurate pose estimation of agile-legged robots, which has been a challenging problem to tackle. Our framework leverages the benefits of both RGB-D and event cameras to achieve robust and accurate pose estimation, even during dynamic maneuvers such as jumping and landing a quadruped robot, the Mini-Cheetah. Our major contributions are threefold: Firstly, we introduce an adaptive time surface (ATS) method that addresses the whiteout and blackout issue in conventional time surfaces by formulating pixel-wise decay rates based on scene complexity and motion speed. Secondly, we develop an effective pixel selection method that directly samples from event data and applies sample filtering through ATS, enabling us to pick pixels on distinct features. Lastly, we propose a nonlinear pose optimization formula that simultaneously performs 3D-2D alignment on both RGB-based and event-based maps and images, allowing the algorithm to fully exploit the benefits of both data streams. We extensively evaluate the performance of our framework on both public datasets and our own quadruped robot dataset, demonstrating its effectiveness in accurately estimating the pose of agile robots during dynamic movements.