Futuristic applications of intelligent transportation systems (ITS) highly rely on ad-hoc connectivity between the stochastic vehicular networks (ground and airborne). Message routing in ITS faces several challenges in the dynamic environment of highly mobile networks in the form of obstacles, propagation, and stability of the connection. Unlike vehicular ad-hoc networks (VANETs), flying ad-hoc networks (FANETs) have a flexible and robust configuration with line-of-sight links, and can provide message relaying services to VANETs. However, constant FANET usage depletes residual energy, leading to a shorter network lifetime. In this study, we propose UniFaVa, a routing scheme that considers a combined and unified paradigm of FANETs and VANETs, where a routing decision prefers a higher transmission rate of unmanned aerial vehicles (UAVs) with ample residual energy as a relay. The proposed scheme guarantees the reliability of a complete transmission by analytically predicting the connectivity time. Moreover, an analytical approach is formulated for the proposed multi-objective optimal routing using hypervolume. Our extensive simulation results using real traffic traces of Seoul and New York City from OpenStreetMap and simulation of urban mobility (SUMO) indicate significant achievements over the three existing contemporary routing methods. The proposed UniFaVa multi-objective optimal routing achieves a packet delivery ratio of 90% and a connectivity time of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3\sim 6$</tex-math></inline-formula> sec for established multi-hop routes, and short hop distances for a reliable propagation with only one extra hop on average.