We explore the cosmological signatures associated with the twin baryons, electrons, photons and neutrinos in the Mirror Twin Higgs framework. We consider a scenario in which the twin baryons constitute a subcomponent of dark matter, and the contribution of the twin photon and neutrinos to dark radiation is suppressed due to late asymmetric reheating, but remains large enough to be detected in future cosmic microwave background (CMB) experiments. We show that this framework can lead to distinctive signals in large scale structure and in the cosmic microwave background. Baryon acoustic oscillations in the mirror sector prior to recombination lead to a suppression of structure on large scales, and leave a residual oscillatory pattern in the matter power spectrum. This pattern depends sensitively on the relative abundances and ionization energies of both twin hydrogen and helium, and is therefore characteristic of this class of models. Although both mirror photons and neutrinos constitute dark radiation in the early universe, their effects on the CMB are distinct. This is because prior to recombination the twin neutrinos free stream, while the twin photons are prevented from free streaming by scattering off twin electrons. In the Mirror Twin Higgs framework the relative contributions of these two species to the energy density in dark radiation is predicted, leading to testable effects in the CMB. These highly distinctive cosmological signatures may allow this class of models to be discovered, and distinguished from more general dark sectors.