The hyperfine structure of the transitions in the (X,v′′=0→(B,c),v′=2) band system in 39K85Rb and 39K87Rb is studied by using several selective Doppler-free spectroscopy techniques. Significant splitting of the line profiles is observable for the B1Π state levels coupled to the c3Σ+ levels through spin–orbit interactions. The splitting is the result from an interplay between spin–spin, spin–rotation, spin–orbit interactions and the Fermi-contact interaction between the electron’s spin and the nuclear spins. Energy shifts of the perturbed levels were analyzed and modeled within the effective Hamiltonian approach. Molecular and coupling constants were determined, which successfully model the experimental observations. Although the highest experimental resolution of 50 MHz was not sufficient to resolve entirely the hyperfine structure, the model successfully explains the line broadening in 39K85Rb and the line splitting in 39K87Rb.