Studies examining the potential effects of bilingualism on interference suppression show inconsistent results. Our study approaches this topic by distinguishing two potential subcomponents within interference suppression (i.e., Stimulus-Stimulus and Stimulus-Response conflict). We investigated the two subcomponents through their operationalisation in different tasks and examined the role of language proficiency in modulating it. A sample of 111 young adult participants performed four non-linguistic cognitive tasks measuring both visual and auditory domains of cognitive control. Bilinguals outperformed monolinguals in tasks involving Stimulus-Stimulus conflict, but showed comparable performance in tasks involving Stimulus-Response conflict. Specific effects of language proficiency on cognitive control were observed: group differences in auditory inhibition and visual orienting were only observed between high-proficient bilinguals and monolinguals. Taken together, types of conflicts involved in interference tasks and language proficiency could differentially affect performance in monolinguals and bilinguals.