We report measurements of charge configurations and charge transfer dynamics in a hybrid single-electron box composed of aluminum and copper. We used two single-electron transistors (SETs) to simultaneously read out different parts of the box, enabling us to map out stability diagrams of the box and identify various charge transfer processes in the box. We further characterized the elastic cotunneling in the box, which is an important source of error in electron turnstiles consisting of hybrid SETs, and found that the rate was as low as 1 Hz at degeneracy and compatible with theoretical estimates for electron tunneling via virtual states in the central superconducting island of the box.