We propose an adaptive interference avoidance scheme that enhances the performance of ZigBee networks by adapting ZigBees' transmissions to measured wireless local area network (WLAN) interference. Our proposed algorithm is based on a stochastic analysis of ZigBee operation that is interfered with by WLAN transmission, given ZigBee and WLAN channels are overlaid in the industrial, scientific, and medical (ISM) band. We assume that WLAN devices have higher transmission power than ZigBee devices. Then, the high transmission power of WLAN devices causes the capture effect when WLAN and ZigBee transmit simultaneously. On the other hand, ZigBee performs backoff during clear channel assessment (CCA) operation if the WLAN is transmitting its frames on the channel. We adopt a widely used WLAN queueing/transmission model that is based on a Markov chain concept. We model a ZigBee device's operation using the Markov chain that includes WLAN interference statistically derived from the WLAN queueing/transmission model. Our proposed algorithm is evaluated in a simulated ZigBee network in the presence of varying WLAN interference. Numerical results show that our WLAN interference mitigation scheme finds the ZigBee control parameters, among a candidate set, which enhances ZigBee network performance compared to the conventional ZigBee operation.