Full duplex (FD) communications, which increases spectral efficiency through simultaneous transmission and reception on the same frequency band, is a promising technology to meet the demand of next generation wireless networks. In this paper, we consider the application of such FD communication to self-backhauled small cells. We consider a FD capable small cell base station (BS) being wirelessly backhauled by a FD capable macro-cell BS. FD communication enables simultaneous back-haul and access transmissions at small cell BSs, which reduces the need to orthogonalize allocated spectrum between access and backhaul. However, in such simultaneous operations, all the links experience higher interference, which significantly suppresses the gains of FD operations. We propose an interference-aware scheduling method to maximize the FD gain across multiple UEs in both uplink and downlink directions, while maintaining a level of fairness between all UEs. It jointly schedules the appropriate links and traffic based on the back-pressure algorithm, and allocates appropriate transmission powers to the scheduled links using Geometric Programming. Our simulation results show that the proposed scheduler nearly doubles the throughput of small cells compared to traditional half-duplex self-backhauling, even when the uplink/downlink traffic is asymmetric.