Complete studies of the radiative processes of thermal emission from the amorphous dust from microwave through far-infrared wavebands are presented by taking into account, self-consistently for the first time, the standard two-level systems (TLS) model of amorphous materials. The observed spectral energy distributions (SEDs) for the Perseus molecular cloud (MC) and W 43 from microwave through far-infrared are fitted with the SEDs calculated with the TLS model of amorphous silicate. We have found that the model SEDs reproduce the observed properties of the anomalous microwave emission (AME) well. The present result suggests an alternative interpretation for the AME being carried by the resonance emission of the TLS of amorphous materials without introducing new species. Simultaneous fitting of the intensity and polarization SEDs for the Perseus MC and W 43 are also performed. The amorphous model reproduces the overall observed feature of the intensity and polarization SEDs of the Perseus MC and W 43. However, the model's predicted polarization fraction of the AME is slightly higher than the QUIJOTE upper limits in several frequency bands. A possible improvement of our model to resolve this problem is proposed. Our model predicts that interstellar dust is amorphous materials with very different physical characteristics compared with terrestrial amorphous materials.