This paper presents the analysis of integrated voice and data cellular networks with channel borrowing. Our considered system gives higher priority to handoff calls over new calls from users' point of view and reflects each characteristics of voice and data traffic types. Data handoff calls can wait in a queue while they are in handoff areas if there are no channels available. Voice handoff calls can borrow at most l channels from data calls if there are no idle channels upon their arrivals. We mathematically model this system by applying queueing theory. Then, we analyze its performance to derive the forced termination probability of data handoff calls, the blocking probabilities of the new and handoff calls of voice and data, and the Laplace Stieltjes transform for the distribution of waiting time in a queue. In numerical results, the analytical results for the mean waiting time of data handoff calls are compared with the simulation results to validate our analytical approach. Our system is also compared with the system where channel borrowing cannot be allowed (nonborrowing system) with respect to the blocking probabilities of the new and handoff calls of voice and data, the forced termination probability of data handoff calls, the mean and the coefficient of variation of the waiting time of data handoff calls.