Our investigation focuses on the performance of full-duplex systems where both nodes simultaneously exchange their signals using a single spectrum for two-way communication. To maximize the achievable sum rate (ASR) for full-duplex systems in multispectrum environments, we address a new selection strategy that considers the channel state of both nodes. The ASR for a multispectral bidirectional full-duplex (M-BFD) system is obtained using the proposed selection strategy and compared with conventional multispectral bidirectional half-duplex (M-BHD) systems. We derive the ASR as closed-form expressions and quantify the effect of selection diversity on the ASRs for M-BFD and M-BHD systems. In addition, we present practical-case Monte Carlo simulation results by considering the effects of self-interference (SI) and channel correlation. The numerical results show that the ASR gain for M-BFD is larger than that for M-BHD.