This paper gives the models for cross-layer mapping from services at the application-layer to multiple connections at the transport-layer then to multiple paths at the network-layer based on network utility maximization (NUM). This paper also presents the objective of cross-layer mapping from services to paths via connections, which is to allocate the path capacity of users, so that the aggregated utility of users can be globally maximized. For the mapping model, in order to achieve the optimum, a distributed algorithm is proposed which is asymptotically stable, and the equilibrium point is optimum. Simulation results verify the convergence of the proposed algorithm. Security and reliability of the mapping are also analyzed theoretically. The probabilities with which a service can be successfully completed are obtained when there are interceptions and distributed attacks in networks. Simulation examples are finally given to show the high security and reliability of the multi-to-multi mapping.