Ulysses encountered two separate sequences of corotating interaction regions (CIRs) in 1992--3 and 1996--7 when the spacecraft was in the southern and northern solar hemispheres, respectively. We have examined magnetometer data from one event observed in each hemisphere. Using two separate analytical methods we provide evidence for the magnetic field vectors within these CIRs being strongly confined to a series of near-parallel planes. The distribution of the field within the interaction region is characteristic of that observed in planar magnetic structures. This planar order is evident over both small (3-hour) and large (whole event) scales. The CIRs display opposed north-south tilts that are consistent with previous authors' analysis of solar wind plasma data. These results are in direct agreement with the tilted dipole model of three-dimensional corotating stream interactions. ¿ 2000 American Geophysical Union