Today urban road network of a modern city can include several subnets. Indeed, bus lanes form a transit subnet available only for public vehicles. Toll roads form a subnet, available only for drivers who ready to pay fees for passage. The common aim of developing such subnets is to provide better urban travel conditions for public vehicles and toll-paying drivers. The present paper is devoted to the equilibrium traffic flow assignment problem in a multi-subnet urban road network. We formulate this problem as a non-linear optimization program and prove that its solution corresponds to the equilibrium traffic assignment pattern in a multi-subnet road network. Moreover, we prove that obtained equilibrium traffic assignment pattern guarantees less or equal travel time for public vehicles and toll-paying drivers than experienced by all other vehicles. The findings of the paper contribute to the traffic theory and give fresh managerial insights for traffic engineers.