Wireless Mesh Networks (WMNs) are considered self-organizing, self-healing, and self-configuring networks. Despite these exciting features, WMNs face several routing challenges including scalability, reliability and link failures, mobility, flexibility, and other network management issues. To address these challenges, WMNs need to make programmable to allow modifications of standard techniques to be configured and implemented through software programs that can be resolved by integrating Software Defined Networking (SDN) architecture. SDN, being a cutting-edge technology promises the facilitation of network management as well as routing issues of wireless mesh networks. However, the evolution of the legacy IP-based network model in its entirety leads to technical, operational, and economic problems that can be mitigated by full interoperability between SDN and existing IP devices. This study introduces a Robust Routing Architecture for Hybrid Software-Defined and Wireless Mesh Networks (Soft-Mesh), by systematic and gradual transitioning of WMNs to SDNs in an efficient manner. The main objective of this paper is to suggest improvements to the architecture of the SDN node that allow the implementation of various network functions such as routing, load balancing, network control, and traffic engineering for the hybrid SDN and IP networks. Mininet-WiFi Simulator is used to perform various experiments to evaluate the performance of proposed architecture by creating a hybrid network topology with a varying number of nodes that is 50, 100, 150, 200, and 250 including SDN hybrid and legacy nodes with varying proportion of SDN hybrid and legacy nodes. Results are taken for the average UDP throughput, end-to-end delay, packet drop ratio, and routing overhead while comparing with traditional routing protocols including Optimized Link State Routing (OLSR) and Better Approach to Mobile Adhoc Networking (BATMAN) and with existing hybrid SDN/IP routing architectures including Hakiri and wmSDN. The analysis of simulation results shows that the proposed architecture Soft-Mesh outperforms in terms of the aforementioned performance metrics than the traditional and exiting hybrid routing protocols. Soft-Mesh gives 50% to 70% improved results concerning the incremental proportion of SDN hybrid nodes.