Neutron production cross sections have been measured from 290 MeV/nucleon C and 600 MeV/nucleon Ne interacting in a slab of simulated Martian regolith/polyethylene composite, and from 400 MeV/nucleon Ne interacting in a section of wall materials from the International Space Station. Neutron spectra were measured at 7 angles between 5 degrees and 80 degrees, and for neutron energies 5 MeV and greater. Spectra at forward angles are dominated by the breakup of the projectile, whereas spectra at back angles show the typical exponential falloff with energy that is indicative of decay from the overlap region and the target remnant. The measured total neutron production cross sections indicate that the regolith/polyethylene composite may be a more effective shielding material than the ISS wall materials, in terms of the number of neutrons produced.