Magnetism is a key driving force controlling several thermodynamic and kinetic properties of Fe-Cr systems. We present a tight-binding model for Fe-Cr, where magnetism is treated beyond the usual collinear approximation. A major advantage of this model consists in a rather simple fitting procedure. In particular, no specific property of the binary system is explicitly required in the fitting database. The present model is proved to be accurate and highly transferable for electronic, magnetic, and energetic properties of a large variety of structural and chemical environments: surfaces, interfaces, embedded clusters, and the whole compositional range of the binary alloy. The occurrence of noncollinear magnetic configurations caused by magnetic frustrations is successfully predicted. The present tight-binding approach can apply to other binary magnetic transition-metal alloys. It is expected to be particularly promising if the size difference between the alloying elements is rather small and the electronic properties prevail.