We have investigated the single-molecule magnets [Mn(III) (2) (5-Brsalen)(2) (MeOH)(2) M(III) (CN)(6) ]NEt(4) (M=Os (1) and Ru (2); 5-Brsalen=N,N'-ethylenebis(5-bromosalicylidene)iminate) by frequency-domain Fourier-transform terahertz electron paramagnetic resonance (THz-EPR), inelastic neutron scattering, and superconducting quantum interference device (SQUID) magnetometry. The combination of all three techniques allows for the unambiguous experimental determination of the three-axis anisotropic magnetic exchange coupling between Mn(III) and Ru(III) or Os(III) ions, respectively. Analysis by means of a spin-Hamiltonian parameterization yields excellent agreement with all experimental data. Furthermore, analytical calculations show that the observed exchange anisotropy is due to the bent geometry encountered in both 1 and 2, whereas a linear geometry would lead to an Ising-type exchange coupling.