Simplifying complex computational geometries, also called defeaturing, is essential in industrial simulation pipelines. Defeaturing simplifies the meshing process and reduces the computational complexity of the simulation. Standard defeaturing methods typically rely on geometric criteria and ignore the underlying physics. In contrast, analysis-aware defeaturing offers a posteriori error estimates for geometry simplifications. It does so by combining the defeatured simulation output with the exact geometry information to guide the process. Introduced by Buffa, Chanon, and Vázquez for a single geometrical feature subject to Neumann boundary conditions in Poisson problems, the analysis-aware defeaturing framework has since been extended to various settings: multiple Neumann features in linear elasticity and Stokes flow problems, features subject to Dirichlet conditions, goal-oriented estimates, and adaptivity in combination with a posteriori estimates for the numerical error. However, the latter works only deal with geometrical features located on the boundary of the domain. In this work, we consider geometry simplifications of complex material interfaces within a computational domain. Even when interfaces are handled using immersed methods, accurately resolving complex features still requires expensive quadrature rules. Consequently, defeaturing remains an effective means of reducing the overall computational cost. In this context, we derive a reliable a posteriori estimator for the combined defeaturing and numerical error for a Poisson model problem with discontinuous diffusion coefficients. To capture the numerical component of the error, we employ a standard equilibrated flux reconstruction. To address the defeaturing error, we develop a reliable indicator by adapting the arguments from the boundary feature case to the interface case. In particular, we prove that the indicator's effectivity index is independent of the feature's size. This robustness is crucial for comparing features of different scales. Finally, we validate our approach through extensive numerical experiments.