This paper studies a backscatter assisted wireless powered communication network (BAWPCN) with two users, which can work in the backscatter communication (BackCom) and harvest-then-transmit (HTT) modes, respectively. The user with the HTT mode is also equipped with initial energy stored in its battery with a finite capacity. The proposed model is studied based on a time block, which is divided into two parts, i.e., data backscattering and transmission phases. When the user with the BackCom mode is activated during the data backscattering phase, the user with the HTT mode simultaneously harvests energy from the power station. To maximize the system throughput, we first formulate an optimization problem, which is further solved by a two-stage method which considers both infinite and finite battery capacity cases. The optimal time allocation policy including the tradeoff between data backscattering and transmission phases and maximum energy harvesting time is derived. Numerical results demonstrate the superiority of the proposed model.