Antiferromagnetic layers are a scientifically challenging component in magnetoelectronic devices, such as magnetic sensors in hard-disk heads, or magnetic random-access memory (RAM) elements. In this paper, it is shown that photoelectron emission microscopy (PEEM) is capable of determining the magnetic structure at the interface of ferromagnets and antiferromagnets with high spatial resolution (down to 20 nm). Dichroism effects at the L edges of the magnetic 3d transition metals, using circularly or linearly polarized soft X-rays from a synchrotron source, give rise to a magnetic image contrast. Images, acquired with the PEEM2 experiment at the Advanced Light Source, show magnetic contrast for antiferromagnetic LaFeO3, microscopically resolving the magnetic domain structure in an antiferromagnetically ordered thin film for the first time. Magnetic coupling between LaFeO3 and an adjacent Co layer results in a complete correlation of their magnetic domain structures. From field-dependent measurements, a unidirectional anisotropy resulting in a local exchange bias of up to 30 Oe in single domains could be deduced. The elemental specificity and the quantitative magnetic sensitivity render PEEM a perfect tool to study magnetic coupling effects in multilayered thin-film samples.