The weak inverse mean curvature flow, initially introduced by Huisken and Ilmanen, has been a powerful tool in approaching scalar curvature problems. On the other hand, the analytic and measure-theoretic structure of the inverse mean curvature flow itself draws growing attention recently. In this talk, I will introduce a new theory for the (weak) inverse mean curvature flow inside bounded domains. In our setting, the boundary of the domain plays the role of an outer obstacle, and the hypersurfaces in the flow stick tangentially to the boundary upon contact. We will discuss the geometric behavior of such solutions, the global regularity of level sets, and the relation to the well-posedness of initial value problems.