In this paper, radio resource allocation for mobile terminals (MTs) in a heterogeneous wireless access medium is investigated. Unlike the existing solutions in literature, two types of services are considered in this paper, namely single-network and multi-homing services. In single-network services, an MT is assigned to the best available wireless network, while in multi-homing services an MT utilizes all available wireless access networks simultaneously. With the presence of both services in the heterogeneous wireless access medium, the radio resource allocation objective is of twofold: We aim to find the optimal assignment of MTs with single-network service to the available wireless access networks and to determine the corresponding optimal bandwidth allocation to the MTs with single-network and multi-homing services. The radio resource allocation problem is formulated to guarantee the service quality for both service types. Numerical results are presented to demonstrate the performance of the proposed radio resource allocation scheme.