Using a first-principles approach, we characterize P-b-type defects at Si-SiO2 interfaces by calculating hyperfine parameters for several relaxed structural models. Application to the Pb center at the Si(111)-SiO2 interface, for which the atomic structure is well established, yields good agreement with experiment and validates our approach. We generated model structures for P-b0 and P-b1 by creating defective sites in interface models, obtained previously by attaching tridymite, a crystalline form of SiO2, to Si(001). As a model for the P-b0 center, we took a Si atom of the substrate with an unsaturated dangling bond sticking into a regular  direction of the crystal. The good agreement between calculated and measured hyperfine parameters supports this assignment. For the P-b1 center, we first considered the strained bond model and the oxygen nearest-neighbor model following suggestions in the literature. However, neither of these two models matched the measured hyperfine data. A novel model, in which a silicon dimer is asymmetrically oxidized in its backbonds, yields hyperfine parameters in excellent agreement with experiment and is proposed as the atomic structure of the P-b1 center.