Carbon nanomembranes (CNMs) are a new class of near-2D materials with potential applications ranging from energy storage and generation, through to water and nano-filtration. These nanometer-thin carbon films can be produced by irradiating self assembled mono-layers of organic molecules, e.g. biphenylthiol or terphenylthiol, with low-energy electrons. The structure-property relationships of CNMs are challenging to characterise with traditional experimental techniques alone, largely due to the fragility of the free-standing CNMs. While ion irradiation is traditionally used to modify bulk materials and their surfaces, highly-charged ions can also be used to characterise CNMs by examining the resultant charge state spectra of transmitted ions. Here, a coupled experimental and simulation approach is used to identify candidate atomistic structures from those generated via molecular dynamics (MD) simulations, by comparing the predicted elastic constants and transmitted ion charge exchange spectra to experiment. The results suggest that CNMs may have an open porous structure, with an under-coordinated carbon network that may be stabilised by hydrogen or oxygen groups when exposed to atmospheric conditions. Looking forward, the candidate CNM structures may be valuable for future computational studies, such as to further elucidate water permeation mechanisms during filtration.