Abstract: Charge asymmetry in the processes e(+)e(-) -> mu(+)mu(-)gamma and e(+)e(-) -> pi(+)pi(-)gamma 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/c(2). It is compared to the expectation from QED for e(+)e(-) -> mu(+)mu(-)gamma, and from theoretical models for e(+)e(-) -> pi(+)pi(-)gamma. A clear interference pattern is observed in e(+)e(-) -> pi(+)pi(-)gamma, particularly in the vicinity of the f(2)(1270) resonance. The inferred rate of lowest-order FSR production is consistent with the QED expectation for e(+)e(-) -> mu(+)mu(-)gamma, and is negligibly small for e(+)e(-) -> pi(+)pi(-)gamma.