In this paper, we consider a two-way cognitive cooperative radio network (TW-CCRN) with hybrid interweaveunderlay spectrum access in the presence of imperfect spectrum sensing. Power allocation strategies are proposed that maximize the sum-rate and minimize the outage probability of the hybrid TW-CCRN. Specifically, based on the state of the primary network (PN), fading conditions, and system parameters, suitable power allocation strategies subject to the interference power constraint of the PN are derived for each transmission scenario of the hybrid TW-CCRN. Given the proposed power allocation strategies, we analyze the sum-rate and outage probability of the hybrid TW-CCRN over Rayleigh fading taking imperfect spectrum sensing into account. Numerical results are presented to illustrate the effect of the arrival rate, interference power threshold, transmit power of the PN, imperfect spectrum sensing, and maximum total transmit power on the sum-rate and outage probability of the hybrid TW-CCRN. OAPA