Integrated access and backhaul (IAB) facilitates cost-effective deployment of millimeter wave(mmWave) cellular networks through multihop self-backhauling. Full-duplex (FD) technology, particularly for mmWave systems, is a potential means to overcome latency and throughput challenges faced by IAB networks. We derive practical and tractable throughput and latency constraints using queueing theory and formulate a network utility maximization problem to evaluate both FD-IAB and half-duplex(HD)-IAB networks. We use this to characterize the network-level improvements seen when upgrading from conventional HD IAB nodes to FD ones by deriving closed-form expressions for (i) latency gain of FD-IAB over HD-IAB and (ii) the maximum number of hops that a HD- and FD-IAB network can support while satisfying latency and throughput targets. Extensive simulations illustrate that FD-IAB can facilitate reduced latency, higher throughput, deeper networks, and fairer service. Compared to HD-IAB,FD-IAB can improve throughput by 8x and reduce latency by 4x for a fourth-hop user. In fact, upgrading IAB nodes with FD capability can allow the network to support latency and throughput targets that its HD counterpart fundamentally cannot meet. The gains are more profound for users further from the donor and can be achieved even when residual self-interference is significantly above the noise floor.