We report a temperature-dependent x-ray diffraction study of critical behavior of sublattice order in thin epitaxial FeCo(001) films grown on MgO(001). The quantitative analysis of the diffraction profiles reveals a crossover phenomenon between strong-field and weak-field critical adsorption which occurs at a reduced temperature t(1)=1.3x10(-3). We demonstrate that this scenario gives a first experimental access to the universal critical exponent eta(perpendicular to) which governs the spatial decay of critical fluctuations perpendicular to the surface. We find eta(perpendicular to)=0.86(5).