Observation by electron spin resonance of the full angular dependence of the hyperfine (hf) interaction spectrum associated with the interfacial P-b1 defect in thermal (100)Si/SiO2 shows that the dominant interaction arises from a single Si-29 atom. The hf tensor displays weakly monoclinic I (nearly axial) symmetry, with the principal axes of the g and hf tensors coinciding. Observation of an identical hf structure consolidates the presence of the P-b1 defect in porous Si. A molecular orbital analysis indicates that the unpaired electron resides for similar to 58% in a single unpaired Si hybrid orbital, found to be 14% s-like and 86% p-like, with the p-orbital pointing closely along a <211> direction at 35.26 degrees with the  interface normal. Excluding oxygen as an immediate part of the defect, the results establish the P-b1 core as a tilted (similar to 20 degrees about <011>) Si-3=Si . unit. The moiety is pictured as part of a strained Si-Si dimer near the interface.