  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 system's capabilities,
we study cold collisions between ammonia ($^{14}$ND$_{3}$ and $^{15}$ND$_{3}$)
molecules and rubidium ($^{87}$Rb and $^{85}$Rb) atoms.
