Using a first-principles approach, we characterize dangling bond defects at Si-SiO2 interfaces by calculating hyperfine parameters for several relaxed structures; Interface models, in which defect Si atoms remain close to crystalline sites of the substrate upon relaxation, successfully describe P-b and P-b0 defects at (111) and (100) interfaces, respectively. On the basis of calculated hyperfine parameters, we discard models of the P-b1 defect containing a first neighbor shell with an O atom or a strained bond. A novel model consisting of an asymmetrically oxidized dimer yields hyperfine parameters in excellent agreement with experiment and is proposed as the structure of the P-b1 center.