This paper considers routing and link scheduling in a two-tier wireless Internet of Things (IoT) network. The first tier consists of routers that communicate via active Radio Frequency (RF) transmissions. The second tier consists of passive tags that backscatter ambient RF signals from routers. Our objective is to maximize the network throughput at both tiers. To this end, we outline a Mixed Integer Linear Program (MILP) that jointly optimizes the active time of RF links and backscatter links, and traffic over links. We also present a heuristic called Algorithm-Transmission-Set-Generator (ALGO-TSG) to compute transmission sets. Moreover, we also outline a heuristic called Centralized Max-Flow (CMF) to maximize network throughput by jointly considering routing and link scheduling. The results show that (i) the network throughput achieved by ALGO-TSG at both tiers is 29.80% higher as compared to the case without backscattering, and, (ii) the throughput of CMF is on average 21.36% lower t