In this talk, we will discuss a recent result concerning variational problems that encompass both bulk and interface energies, which are used to describe a broad spectrum of phenomena in applied sciences. A key feature of these models is the presence of a free boundary whose regularity is intricate to establish due to the interaction between the bulk term and the perimeter term. We will present an $\varepsilon$-regularity result for almost-minimizers of a class of problems with bulk energy of Dirichlet type and surface energy exhibiting anisotropic Finsler behavior, defined by an ellipsoidal density that is Hölder continuous with respect to the position variable. This presentation is based on joint work with L. Esposito and L. Lamberti.