The Atmospheric Chemistry Experiments Fourier Transform Spectrometer on the SCISAT satellite has been measuring infrared transmission spectra of Earth during Solar occultations since 2004. We use these data to build an infrared transit spectrum of Earth. Regions of low atmospheric opacity, known as windows, are of particular interest, as they permit observations of the planets lower atmosphere. Even in the absence of clouds or refraction, imperfect transmittance leads to a minimum effective thickness of $h_{min} approx 4$ km in the 10--12$mu$m opacity window at a spectral resolution of $R=10^3$. Nonetheless, at $R=10^5$, the maximum transmittance at the surface is around 70%. In principle, one can probe the troposphere of an Earth-like planet via high-dispersion transit spectroscopy in the mid-infrared; in practice aerosols and/or refraction likely make this impossible. We simulate the transit spectrum of an Earth-like planet in the TRAPPIST-1 system. We find that a long-term near-infrared campaign with JWST could readily detect CO$_2$, establishing the presence of an atmosphere. A mid-IR campaign or longer NIR campaign would be more challenging, but in principle could detect H$_2$O and the biosignatures O$_3$ and CH$_4$.