Transmission radiography using MeV-class radiation is a powerful non-destructive method for determining the elemental composition. Radiography is typically performed using either neutrons or photons, but neither of these probes is universally applicable. We experimentally demonstrate that a significant improvement in the contrast for small elemental variations in object composition can be realized by combining the multiple monoenergetic neutron and photon transmission radiography techniques. The multimodal source is based on deuteron-driven low-energy nuclear reactions that produces both neutrons and photons at discrete energies. The neutron time-of-flight technique was employed to measure the transmission over a broad range of neutron energies and was combined with spectroscopic photon transmission. This work demonstrates the use of a single, multi-particle, multiple monoenergetic radiation source and a single radiation detector type to simultaneously perform neutron and photon spectroscopic radiography. Four different material identification metrics are employed, which show a factor of three or higher increase in sensitivity to changes in material composition when compared to the traditional dual-energy photon radiography, and are in agreement with simulations that establish the direct correspondence to known photon and neutron interaction cross sections. Further, the ability to infer the presence of objects consisting of impure elements, layers of different elements, or non-natural isotope concentrations is demonstrated.