We study the combination of the hyperfine and Zeeman structure in the spin-orbit coupled A(1)Sigma(+)(u) = b(3)Pi(u) complex of Rb-87(2). For this purpose, absorption spectroscopy at a magnetic field around B = 1000 G is carried out. We drive optical dipole transitions from the lowest rotational state of an ultracold Feshbach molecule to various vibrational levels with 0(+) symmetry of the A - b complex. In contrast to previous measurements with rotationally excited alkali-dimers, we do not observe equal spacings of the hyperfine levels. In addition, the spectra vary substantially for different vibrational quantum numbers, and exhibit large splittings of up to 160 MHz, unexpected for 0(+) states. The level structure is explained to be a result of the repulsion between the states 0(+) and 0(-) of b(3)Pi(u), coupled via hyperfine and Zeeman interactions. In general, 0(-) and 0(+) have a spin-orbit induced energy spacing Delta, that is different for the individual vibrational states. From each measured spectrum we are able to extract Delta, which otherwise is not easily accessible in conventional spectroscopy schemes. We obtain values of Delta in the range of +/- 100 GHz which can be described by coupled channel calculations if a spin-orbit coupling is introduced that is different for 0(-) and 0(+) of b(3)Pi(u).