Charge asymmetry in the processes e+e-→μ+μ-γ and e+e-→π+π-γ is measured using 232 fb-1 of data collected with the BABAR detector at e+e- center-of-mass energies near 10.58 GeV. An observable is introduced and shown to be very robust against detector asymmetries while keeping a large sensitivity to the physical charge asymmetry that results from the interference between initial- and final-state radiation (FSR). The asymmetry is determined as a function of the invariant mass of the final-state tracks from production threshold to a few GeV/c2. It is compared to the expectation from QED for e+e-→μ+μ-γ, and from theoretical models for e+e-→π+π-γ. A clear interference pattern is observed in e+e-→π+π-γ, particularly in the vicinity of the f2(1270) resonance. The inferred rate of lowest-order FSR production is consistent with the QED expectation for e+e-→μ+μ-γ, and is negligibly small for e+e-→π+π-γ.