The use of semi-autonomous Unmanned Aerial Vehicles (UAVs or drones) to support emergency response scenarios, such as fire surveillance and search-and-rescue, has the potential for huge societal benefits. Onboard sensors and artificial intelligence (AI) allow these UAVs to operate autonomously in the environment. However, human intelligence and domain expertise are crucial in planning and guiding UAVs to accomplish the mission. Therefore, humans and multiple UAVs need to collaborate as a team to conduct a time-critical mission successfully. We propose a meta-model to describe interactions among the human operators and the autonomous swarm of UAVs. The meta-model also provides a language to describe the roles of UAVs and humans and the autonomous decisions. We complement the meta-model with a template of requirements elicitation questions to derive models for specific missions. We also identify common scenarios where humans should collaborate with UAVs to augment the autonomy of the UAVs. We introduce the meta-model and the requirements elicitation process with examples drawn from a search-and-rescue mission in which multiple UAVs collaborate with humans to respond to the emergency. We then apply it to a second scenario in which UAVs support first responders in fighting a structural fire. Our results show that the meta-model and the template of questions support the modeling of the human-on-the-loop human interactions for these complex missions, suggesting that it is a useful tool for modeling the human-on-the-loop interactions for multi-UAVs missions.