This paper analyzes an emerging architecture of cellular network utilizing both planar base stations uniformly distributed in Euclidean plane and base stations located on roads. An example of this architecture is that where, in addition to conventional planar cellular base stations and users, vehicles also play the role of both base stations and users. A Poisson line process is used to model the road network and, conditionally on the lines, linear Poisson point processes are used to model the vehicles on the roads. The conventional planar base stations and users are modeled by independent planar Poisson point processes. The joint stationarity of the elements in this model allows one to use Palm calculus to investigate statistical properties of such a network. Specifically, this paper discusses two different Palm distributions, with respect to the user point processes depending on its type: planar or vehicular. We derive the distance to the nearest base station, the association of the typical users, and the coverage probability of the typical user in terms of integral formulas. Furthermore, this paper provides a comprehensive characterization of the performance of all possible cellular transmissions in this setting, namely vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), infrastructure-to-vehicle (I2V), and infrastructure-to-infrastructure (I2I) communications.