In this letter, we propose an opportunistic source selection based two-way cooperative ambient backscatter communication (CABC) system, in which two sources convey information to each other via a decode-and-forward enabled relay node and the tag embedded in the relay utilizes the power difference produced by the two hops to accomplish backscatter communication (BC) concurrently. The proposed system can achieve the bidirectional information flow for both the relaying transmission (RT) and BC at the same time. The analytical results of the outage probabilities for both RT and BC are derived. Numerical results verify the theoretical analysis and show that the proposed scheme can increase the throughput of the BC while maintaining the same power consumption and not degrading the performance of RT, compared to the existing one-way CABC system.