The hyperfine splitting in hydrogenlike ²⁰⁹Bi, ²⁰³Tl, and ²⁰⁵Tl is calculated with the nuclear magnetization determined from experimental data on the hyperfine splitting in the corresponding muonic atoms. The single-particle and configuration-mixing nuclear models are considered. The QED corrections are taken into account for both electronic and muonic atoms. The obtained results are compared with other calculations and with experiment.