The Quality of Service (QoS) of wireless Internet access that could be provided to multihop wireless networks, so-called mobile ad hoc networks (MANETs), is highly dependent on the quality of the design of the intermediate facility that will integrate MANET and the Internet. This facility is equipped with a hybrid mechanism being able to fulfill the working requirements of MANET and the Internet so that it can connects to either one of these orthogonal network architectures. The architecture that we propose in order to provide MANET nodes with Internet access utilizes fixed gateways (or access points) and exploits the mobility capability of additional mobile ones. Since Internet access to MANET nodes is provided through mobile gateways, the quality of such service depends on the selection procedure used by MANET nodes to choose the most convenient mobile gateways and register with. In this paper, we suggest to use a hybrid criterion based on the weighted sum of the Euclidean distance between MANET nodes and mobile gateways, and the load of mobile gateways, defined as the number of MANET nodes currently registered with them. Moreover, the sum of the weights is normalized to one, where each weight measures the level of interest of the corresponding criterion in the hybrid one. Simulation results show that the hybrid criterion has an impact on the quality of wireless Internet access service depending on the level of interest assigned to each of the Euclidean distance and load criteria in the weighted sum.