The structural properties of the phase coexistence of chemically ordered L1(0) and chemically disordered structures within binary alloys are investigated, using the NiMn system as an example. Theoretical and numerical predictions of the signatures that one might expect in data from local and extended probes are presented in an attempt to explain the presence of antiferromagnetism in NiMn when no L1(0) signatures appear in diffraction data. Two scenarios are considered. In the first scenario, the tetragonal L1(0) structure and fcc chemically disordered structure are distributed evenly into uncorrelated domains of specified average diameter. The diffraction limit, below which the two structures can only be distinguished using a local probe, is quantified with respect to the domain diameter by applying straightforward diffraction analysis. In the second scenario, domains with chemical ordering oriented in different directions are required to maintain their atomic coherence with each other. A numerical treatment is used to illustrate the long-range strain that results from elastic energy considerations, and the effects on the structure factor (extended probe) and pair distribution function (local probe) are investigated.