The interacting boson fermion-fermion model is employed in the analysis of the positive-parity doublet bands in 134Pr. It is shown that stable triaxial deformation gives rise to the experimentally observed crossing between the yrast and yrare bands built on the h11/2h11/2 configuration. The collective structure of the yrast band is basically built on the ground-state band of the triaxial core, whereas the collective structure of the yrare band is predominantly based on the band of the core. The mixing between the two bands increases with angular momentum. A constant energy spacing between the two lowest positive-parity bands is predicted in other odd-odd N = 75 nuclei with -soft potential energy surfaces.