We present experimental evidence for a three-dimensional noncollinear antiferromagnetic spin structure in ultrathin single-crystalline fcc Fe₅₀Mn₅₀ layers using magnetic circular dichroism photoelectron emission microscopy and x-ray magnetic linear dichroism. Layer-resolved as-grown domain images of epitaxial trilayers grown on Cu(001) in which FeMn is sandwiched between ferromagnetic layers with different easy axes reveal the presence of antiferromagnetic spin components in the film plane and normal to the film plane. An FeMn spin structure with no collinear order in the film plane is consistent with the absence of x-ray magnetic linear dichroism in Fe L₃ absorption in FeMn/Co bilayers.