We probe the local magnetic properties of interfaces between the insulating ferromagnet EuS and the topological insulator Bi₂Se₃ using low energy muon spin rotation (LE-μSR). We compare these to the interface between EuS and the topologically trivial metal, titanium. Below the magnetic transition of EuS, we detect strong local magnetic fields which extend several nm into the adjacent layer and cause a complete depolarization of the muons. However, in both Bi₂Se₃ and titanium we measure similar local magnetic fields, implying that their origin is mostly independent of the topological properties of the interface electronic states. In addition, we use resonant soft x-ray angle resolved photoemission spectroscopy (SX-ARPES) to probe the electronic band structure at the interface between EuS and Bi₂Se₃. By tuning the photon energy to the Eu antiresonance at the Eu M₅ pre-edge we are able to detect the Bi₂Se₃ conduction band, through a protective Al₂O₃ capping layer and the EuS layer. Moreover, we observe a signature of an interface-induced modification of the buried Bi₂Se₃ wave functions and/or the presence of interface states.