The passenger flow assignment in the rail transit network is the basis for determining the passenger spatiotemporal distribution and train operation organization plan. In previous studies, the passenger flow assignment problem mainly focused on lines within the same rail system. Few studies focus on lines with the integrated mode of cross-line and skip-stop operation between state and suburban railway due to fewer cases in practice. In this study, passenger congestion and fare policy are taken into account in the generalized travel cost function, and a passenger flow assignment model based on the path-sized logit (PSL) model considering train capacity is proposed. Meanwhile, a schedule-based spatiotemporal digraph is established to search for the shortest spatiotemporal travel path. Furthermore, an improved method of successive averages (MSA) algorithm is designed to solve the proposed model. The proposed model is verified by a numerical example. The sensitivities of three main parameters which influence the results are also analyzed. The results show that the assignment model based on PSL is practicable in integrated operation mode. The higher the passenger’s familiarity with network information, the more accurate the assignment results. State trains are more attractive when the fare is lower than 0.5 CNY/km or the hourly wage is higher than 50 CNY/h.