Fire resistance is a major issue concerning composite materials for safe operation in many industrial sectors. The design process needs to meet safety requirements for buildings and vehicles, where the use of composites has increased. There are several solutions to increasing the flame resistance of polymeric materials, based on either chemical modification or physical additions to the material’s composition. Generally, the used flame retardants affect mechanical properties either in a positive or negative way. The presented research shows the influence of the mixed-mode behavior of epoxy resin. Fracture toughness tests on epoxy resin samples were carried out, to investigate the changes resulting from different inorganic filler contents of aluminum trihydroxide (ATH). Three-point bending and asymmetric four-point bending tests, with different loading modes, were performed, to check the fracture behavior in a complex state of loading. The results showed that the fracture toughness of mode I and mode II was reduced by over 50%, compared to neat resin. The experimental outcomes were compared with theoretical predictions, demonstrating that the crack initiation angle for higher values of KI/KII factor had a reasonable correlation with the MTS prediction. On the other hand, for small values of the factor KI/KII, the results of the crack initiation angle had significant divergences. Additionally, based on scanning electron microscopy images, the fracturing of the samples was presented.