Recently, we determined the detailed energy level structure of the X 1 + , A 1 and a 3 states of AlF that are relevant to laser cooling and trapping experiments [Truppe et al., Phys. Rev. A. 100 (5), 052513 (2019)]. Here, we investigate the b 3 + , v = 0 state of the AlF molecule. A rotationally resolved (1 + 2)-REMPI spectrum of the b 3 + , v = 0 ← a 3 , v = 0 band is presented and the lifetime of the b 3 + , v = 0 state is measured to be 190(2) ns. Hyperfine-resolved, laser-induced fluorescence spectra of the b 3 + , v = 0 ← X 1 + , v = 1 and the b 3 + , v = 0 ← a 3 , v = 0 bands are recorded to determine fine-and hyperfine structure parameters. The interaction between the b 3 + , v = 0 and the nearby A 1 state is studied and the magnitude of the spin-orbit coupling between the two electronic states is derived using three independent methods to give a consistent value of 10(1) cm −1. The triplet character of the A state causes an A → a loss from the main A−X laser cooling cycle below the 10 −6 level.