Measurements of interactions between cold molecules and ultracold atoms can allow for a detailed understanding of fundamental collision processes. These measurements can be done using various experimental geometries including where both species are in a beam, where one species is trapped, or when both species are trapped. Simultaneous trapping offers significantly longer interaction times and an associated increased sensitivity to rare collision events. However, there are significant practical challenges associated with combining atom and molecule systems, which often have competing experimental requirements. Here, we describe in detail an experimental system that allows for studies of cold collisions between ultracold atoms and cold molecules in a dual trap, where the atoms and molecules are trapped using static magnetic and electric fields, respectively. As a demonstration of the systems capabilities, we study cold collisions between ammonia ($^{14}$ND$_{3}$ and $^{15}$ND$_{3}$) molecules and rubidium ($^{87}$Rb and $^{85}$Rb) atoms.
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