Infrared solar occultation measurements are well established for remote sensing of Earth's atmosphere, and the corresponding primary transit spectroscopy has turned out to be valuable for characterization of extrasolar planets. Our objective is an assessment of the detectability of molecular signatures in Earth's transit spectra.To this end, we take a limb sequence of representative cloud-free transmission spectra recorded by the space-borne ACE-FTS Earth observation mission (Hughes et al., ACE infrared spectral atlases of the Earth's atmosphere, JQSRT 2014) and combine these spectra to the effective height of the atmosphere. These data are compared to spectra modeled with an atmospheric radiative transfer line-by-line infrared code to study the impact of individual molecules, spectral resolution, the choice of auxiliary data, and numerical approximations. Moreover, the study serves as a validation of our infrared radiative transfer code.The largest impact is due to water, carbon dioxide, ozone, methane, nitrous oxide, nitrogen, nitric acid, oxygen, and some chlorofluorocarbons (CFC11 and CFC12). The effect of further molecules considered in the modeling is either marginal or absent. The best matching model has a mean residuum of 0.4 km and a maximum difference of 2 km to the measured effective height. For a quantitative estimate of visibility and detectability we consider the maximum change of the residual spectrum, the relative change of the residual norm, the additional transit depth, and signal-to-noise ratios for a JWST setup. In conclusion, our study provides a list of molecules that are relevant for modeling transmission spectra of Earth-like exoplanets and discusses the feasibility of retrieval.