Wavelet packet division multiplexing (WPDM) is a multiple signal transmission scheme based on wavelet packets. Due to its bandwidth efficiency, channel assignment flexibility, and inherent security features, it has attracted considerable interest. However, before it can be employed as a practical multiplexing technique, the performance of WPDM in various channels has to be fully investigated. In this paper, we explore the system performance when the channel includes impulsive noise as well as Gaussian noise. After briefly reviewing the system model of WPDM, we derive an expression for the probability of error for WPDM in the presence of both impulsive and Gaussian noise. The derivation extends previous work on the performance of digital communication systems when impulsive noise and Gaussian noise are the causes of error to WPDM. For the purpose of comparison, the performance of a TDM system in the same channel environment in also evaluated. The calculations and corresponding simulation results illustrate that WPDM can provide greater immunity to impulsive noise than TDM. This result is intuitively pleasing since one noise burst, which can destroy one bit in TDM, will be spread over all the channels of a WPDM system. In each channel, the spread effects of the impulsive noise may not be strong enough to cause an error.