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.