A novel polyborosilazane (PBSZ) precursor was synthesized by the reaction of copolysilazane (CPSZ) with dimethylaminoborane (DMAB). The resultant PBSZs were characterized by FT-IR and NMR spectroscopy. It was found that both, BH and NH bonds of DMAB, react with CPSZ leading to boron containing copolysilazanes. The polyborosilazanes were pyrolyzed at 900 °C in argon and the precursor-to-ceramic transformation was studied by TG-MS and FT-IR spectroscopy. The modification of CPSZ with DMAB enhances the cross-linking of the resulting PBSZ, which increases the final ceramic yield from 57.8% to 77.5–80.0%. Finally, the ceramics obtained at 900 °C were subsequently annealed at different temperatures ranging from 1200 to 1800 °C. The heat-treated products were characterized by X-ray powder diffraction and electron microscopy. Accordingly, the resulting SiBCN ceramics exhibit significantly enhanced high-temperature-resistance with respect to decomposition and crystallization as compared with boron-free CPSZ-derived SiCN ceramics. TEM results support that the thermal stability is due to the segregation of a BN(C) phase as interlayer between Si3N4 nanocrystals formed during heat-treatment of SiBCN at T > 1500 °C.