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 travel demand estimation problem in a multi-subnet urban road network. We formulate this problem as a bi-level optimization program and prove that it has a unique solution under quite a natural assumption. Moreover, for the simple case of a road network topology with disjoint routes, we obtain important analytical results that allow us to analyze different scenarios appearing within the travel demand estimation process in a multi-subnet urban road network. The findings of the paper contribute to the traffic theory and give fresh managerial insights for traffic engineers.