The need to engage in multiple tasks simultaneously is often encountered in everyday experience, but coordinating between two or more tasks can lead to impaired performance. Typical investigations of multitasking impairments have focused on the performance of two tasks presented in close temporal proximity on discrete trials; however, such paradigms do not match well with the continuous performance situations more typically encountered outside the laboratory. As a result, the stages of information processing that are affected during multisensory continuous dual tasks and how these changes in processing relate to behavior remain unclear. To address these issues, participants were presented simultaneous rapid visual and auditory stimulus sequences under three conditions: attend visual only, attend auditory only, and dual attention (attend both visual and auditory). Performance, measured in terms of response time and perceptual sensitivity (d′), revealed dual-task impairments only in the auditory task. Neural activity, measured by the ERP technique, revealed that both early stage sensory processing and later cognitive processing of the auditory task were affected by dual-task performance, but similar stages of processing of the visual task were not. Critically, individual differences in neural activity at both early and late stages of information processing accurately rank-ordered individuals based on the observed difference in behavioral performance between the single and dual attention conditions. These results reveal relationships between behavioral performance and the neural correlates of both early and late stage information processing that provide key insights into the complex interplay between the brain and behavior when multiple tasks are performed continuously.