This paper investigates a multi-hop cognitive radio network in terms of end-to-end bit delivery. The network exploits backscatter communication (BackCom) and harvest-then-transmit (HTT) mode in a hybrid manner. Such a network can be used in internet of things (IoT) applications in which IoT users coexist with a primary network (PN) and use the primary spectrum to transmit data in both BackCom and HTT modes. Besides, such users can harvest energy from the primary signals. A novel hybrid backscatter and conventional transmission (HBCT) algorithm is proposed in order to maximize end-to-end bit delivery by jointly optimizing time and power allocations. For this goal, we formulate a non-convex optimization problem. Next, we transform the problem into a convex one and develop a new analytical formulation by which we calculate the optimal power and time allocation in closed-form equations. The numerical results demonstrate the superiority of HBCT compared with current schemes.