Resonances on the lower polariton branch of KI and RbI x e measured by the use of three-photon difference-frequency generation (TP-DFG). From these data the energy of the lowest transverse exciton state is derived. Due to the small linewidth of the resonances it is possible to measure the k-dependent magnetic field splitting of the lower branch for the first time. The results allow to determine the exchange energy, the longitudinal-transverse splitting and the g-values of the uppermost valence band (r, -symmetry) and the lowest conduction band (TZ-symmetry) with much higher accuracy than before.