We use solid metal dealloying to synthesize TaTi/ZrTi nanocomposite thin films with widely differing morphologies of the constituent phases, ranging from particulate to bincontinuously interpenetrating, but comparable characteristic dimensions of microstructure features. We then investigate the indentation and helium implantation response of these composites. Our work shows a systematic dependence of indentation pile-up height on microstructure morphology, which we attribute to morphology-induced differences in strain hardening rates. We also find a reduction in the size and distribution of helium precipitates relative to un-dealloyed materials, which we relate to the characteristic dimensions of microstructure features of the composites. We conclude with a discussion of future prospects for tailoring mechanical and radiation response by changing microstructure morphology in dealloyed composites.