Defects in amorphous-SiO2/Si (a-SiO2/Si) interfaces influence greatly the performance and reliability of Si-based devices. The major interfacial defects that exhibit electronic activity are silicon dangling bonds (so-called P-b defects), which can trap charge carriers and contribute to interfacial charge build-up. In this study, the P-b0 and P-b1 defects at the most technically important a-SiO2/Si(100) interface are investigated quantitatively by using first-principles calculations with realistic interfacial models. Atomistic models of the interface are generated by classical molecular dynamics simulations of Si oxidation with a-SiO2 followed by first-principles structure optimization, and they can reproduce the experimental interfacial properties of the short-range structure parameters, Si oxidation state distribution, and band gap transition. The P-b0 and P-b1 defects are modeled atomistically within the interfacial models, and their g-values and hyperfine parameters are calculated quantitatively by the GIPAW (gauge including projector augmented waves) method. The Fermi contact and hyperfine axis (hf axis) calculated with the Si vacancy model for the P-b0 defect agree well with those obtained experimentally, and the hf axis is coincident with the dangling bond direction determined from the calculated g-tensor and spin density. The Fermi contact and hf axis are calculated for the P-b1 defect with three different models, namely dimer, bridge, and asymmetrically oxidized dimer (AOD), of which the AOD model leads to calculated results that agree well with the experimental ones. However, the AOD model is found to be sensitive to the local structure distortion associated with the softness of the oxygen bridge. What is known as the half AOD is then introduced by deoxidizing one of the two oxygen bridges of the AOD; this may serve as another atomistic model of the P-b1 defect according to the good agreement between the calculated Fermi contact, g-values, and hf axis and the experimental ones. The electronic structures are calculated with the atomistic defect models and show that both defects induce (i) two spin-asymmetric midgap levels in the Si band gap in the neutral state and (ii) spin-symmetric levels in the charged states. The charge transition levels of the defects are calculated with a correction method that is specific to surface/interfacial charge defects, and the calculated levels agree semi-quantitatively with those determined experimentally. The calculated +/0 and 0/- levels are in the Si band gap, with the 0/- level energy being higher than the +/0 one. This implies that both P-b0 and P-b1 defects can trap holes or electrons depending on the position of the Fermi level.