The microwave spectra of four isotopologues of the CHBrF2 center dot center dot center dot HCCH weakly bound dimer have been measured in the 6-18 GHz region using chirped-pulse and Balle-Flygare Fourier-transform microwave spectroscopy. Spectra of (CHBrF2)-C-13-Br-79 and (CHBrF2)-C-13-Br-81 monomers have also been measured, and spectroscopic constants are reported. Measurement of spectra for the Br-79 and Br-81 isotopologues of CHBrF2 complexed with both (C2H2)-C-12 and (C2H2)-C-13 have allowed the determination of a structure with C-5 symmetry for this complex. CHBrF2 interacts with the triple bond of acetylene via a C-H center dot center dot center dot pi contact (R(H center dot center dot center dot pi) = 2.670(8) angstrom) with the Br atom lying in the ab plane, located 3.293(40) angstrom from a hydrogen atom of the HCCH molecule. The structure of CHBrF2 center dot center dot center dot HCCH has been compared with recently studied related acetylene complexes, including a comparison with (and further structural analysis of) the CHClF2 center dot center dot center dot HCCH complex.