Maintaining seamless quality of service (QoS) requirements for ongoing delay sensitive applications during handover processes for Vehicle-to-Infrastructure (V2I) communication over heterogeneous networks is a challenging task. The situation becomes even more challenging to deal with for multi-tier heterogeneous networks with various network sizes. To overcome the above challenges, we propose a multicriteria-based handover algorithm for V2I communications (V2I-MHA) to be used in multi-tier heterogeneous network environments. V2I-MHA selects the most appropriate underlying target network for handover based on QoS profiles of the ongoing applications and services. Moreover, our proposed algorithm filters out the inappropriate candidate networks using a multi-criteria decision-making technique based on Simple Additive Weighting (SAW) approach. However, our approach ensures that the most appropriate candidate network for handover processes is selected not only based on QoS requirements of the ongoing applications, but also on the knowledge of candidate network parameters (e.g. bandwidth, packet latency, packet losses, and service pricing). A multi-mode vehicle On-Board Unit (OBU) containing Long Term Evolution-Advanced (LTEA) and Wi-Fi network interface cards is developed in the Riverbed (previously OPNET) simulator for system performance evaluation. The simulation results show that the proposed V2I-MHA outperforms (in terms of handover failure rate and packet losses) the existing handover methods.