We present a wavelength study of the strong field single electron ionization of molecular iodine near its one-photon B-state resonance at 530 nm. We have previously identified two ionization channels (PRA 95,013410): ionization of the high lying molecular orbitals and ionization of the deep orbitals in I2. We find a resonant enhancement of both channels, although the peak enhancement occurs at different wavelengths for the different channels. Moreover, the branching ratio of the ionization of the deep orbitals shows a dispersion-like function, with the branching ratio of the deep orbitals reaching over 98% at 519 nm. Finally, the branching ratio of double ionization into an excited state of I 2+ 2 as a function of wavelength closely matches the branching ratio of the single ionization of deep orbitals, implying that excitation of molecular ions generally comes about through inner orbital ionization. These findings are inconsistent with current molecular ionization theory.