Aerial robots are transitioning from traditional surveillance and monitoring roles to more advanced tasks involving physical interaction. Despite this progress, physical Human-Aerial Robot Interaction remains largely underexplored due to the complexity and stability-related issues of such platforms. This paper introduces a novel control framework that enables an aerial platform to cooperatively transport an object with a human operator. The control approach is built on a nonlinear model predictive control (NMPC), integrating the dynamic models of the human, the aerial robot, and the transported object. To ensure safe and robust physical interaction, the NMPC is combined with a compliant controller. Additionally, our controller prioritizes forward motion over lateral movements to accommodate the human's natural direction of motion. We validate this framework through indoor flight experiments, demonstrating how a human operator and a fully actuated hexarotor can effectively collaborate to transport a bar. The results highlight the aerial robot's ability to assist the human during physical transportation tasks, enhancing efficiency and comfort.