Barkhausen noise emission in soft magnetic bilayer ribbons has been investigated. The monolithic amorphous Fe73.5Nb3Si13.5B9Cu1/Fe74.5Nb3Si13.5B9 bilayer system was produced by double-nozzle melt-spinning. It was subsequently used to measure the Barkhausen noise emission in the amorphous state as well as in the annealed state as a function of magnetizing voltage. The asymmetry of the Barkhausen noise emission during cyclic magnetization was also investigated. It was found that the amorphous ribbon produces the conventional single burst, whereas the annealed ribbon emits bursts in which Barkhausen noise originating from the different layers can be easily distinguished. Moreover, a gentle asymmetry in the consecutive Barkhausen noise envelopes produced by ascending and descending magnetic fields was detected. The hysteresis loop for the annealed ribbon exhibits a two-step magnetization process in which the contribution of the different layers can be clearly distinguished.