Interactive or collaborative pick-and-place tasks occur during all kinds of daily activities, for example, when two or more individuals pass plates, glasses, and utensils back and forth between each other when setting a dinner table or loading a dishwasher together. In the near future, participation in these collaborative pick-and-place tasks could also include robotic assistants. However, for human-machine and human-robot interactions, interactive pick-and-place tasks present a unique set of challenges. A key challenge is that high-level task-representational algorithms and preplanned action or motor programs quickly become intractable, even for simple interaction scenarios. Here we address this challenge by introducing a bioinspired behavioral dynamic model of free-flowing cooperative pick-and-place behaviors based on low-dimensional dynamical movement primitives and nonlinear action selection functions. Further, we demonstrate that this model can be successfully implemented as an artificial agent control architecture to produce effective and robust human-like behavior during human-agent interactions. Participants were unable to explicitly detect whether they were working with an artificial (model controlled) agent or another human-coactor, further illustrating the potential effectiveness of the proposed modeling approach for developing systems of robust real/embodied human-robot interaction more generally.