(1) Background: The combined n-back + Go/NoGo paradigm was used to investigate whether audiovisual interactions interfere with or facilitate WM. (2) Methods: College students were randomly assigned to perform the working memory task based on either a single (visual or auditory) or dual (audiovisual) stimulus. Reaction times, accuracy, and WM performance were compared across the two groups to investigate effects of audiovisual interactions. (3) Results: With low cognitive load (2-back), auditory stimuli had no effect on visual working memory, whereas visual stimuli had a small effect on auditory working memory. With high cognitive load (3-back), auditory stimuli interfered (large effect size) with visual WM, and visual stimuli interfered (medium effect size) with auditory WM. (4) Conclusions: Audiovisual effects on WM follow the resource competition theory, and the cognitive load of a visual stimulus is dominated by competition; vision always interferes with audition, and audition conditionally interferes with vision. With increased visual cognitive load, competitive effects of audiovisual interactions were more obvious than those with auditory stimuli. Compared with visual stimuli, audiovisual stimuli showed significant interference only when visual cognitive load was high. With low visual cognitive load, the two stimulus components neither facilitated nor interfered with the other in accordance with a speed–accuracy trade-off.