The magnetic structures adopted by the Fe and Sm sublattices in SmFeAsO have been investigated using element-specific x-ray resonant and nonresonant magnetic scattering techniques. Between 110 and 5 K, the Sm and Fe moments are aligned along the c and a directions, respectively, according to the same magnetic representation Gamma(5) and the same propagation vector (1 0 1/2). Below 5 K, the magnetic order of both sublattices changes to a different magnetic structure, and the Sm moments reorder in a magnetic unit cell equal to the chemical unit cell. Modeling of the temperature dependence for the Sm sublattice, as well as a change in the magnetic structure below 5 K, provides clear evidence of a surprisingly strong coupling between the two sublattices, and indicates the need to include anisotropic exchange interactions in models of SmFeAsO and related compounds.