We create atom-molecule dark states in a degenerate Fermi gas of ^{6}Li in both weakly and strongly interacting regimes using two-photon Raman scattering to couple fermion pairs to bound molecular states in the ground singlet and triplet potential. Near the unitarity point in the BEC-BCS crossover regime, the atom number revival height associated with the dark state abruptly and unexpectedly decreases and remains low for magnetic fields below the Feshbach resonance center at 832.2 G. With a weakly interacting Fermi gas at 0 G, we perform precision dark-state spectroscopy of the least-bound vibrational levels of the lowest singlet and triplet potentials. From these spectra, we obtain binding energies of the v^{''}=9, N^{''}=0 level of the a(1^{3}Σ_{u}^{+}) potential and the v^{''}=38, N^{''}=0 level of the X(1^{1}Σ_{g}^{+}) potential with absolute uncertainty as low as 20 kHz. For the triplet potential, we resolve the molecular hyperfine structure.