Connected and autonomous vehicles will play a pivotal role in future Intelligent Transportation Systems (ITSs) and smart cities, in general. High-speed and low-latency wireless communication links will allow municipalities to warn vehicles against safety hazards, as well as support cloud-driving solutions to drastically reduce traffic jams and air pollution. To achieve these goals, vehicles need to be equipped with a wide range of sensors generating and exchanging high rate data streams. Recently, millimeter wave (mmWave) techniques have been introduced as a means of fulfilling such high data rate requirements. In this paper, we model a highway communication network and characterize its fundamental link budget metrics. In particular, we specifically consider a network where vehicles are served by mmWave Base Stations (BSs) deployed alongside the road. To evaluate our highway network, we develop a new theoretical model that accounts for a typical scenario where heavy vehicles (such as buses and lorries) in slow lanes obstruct Line-of-Sight (LOS) paths of vehicles in fast lanes and, hence, act as blockages. Using tools from stochastic geometry, we derive approximations for the Signal-to-Interference-plus-Noise Ratio (SINR) outage probability, as well as the probability that a user achieves a target communication rate (rate coverage probability). Our analysis provides new design insights for mmWave highway communication networks. In considered highway scenarios, we show that reducing the horizontal beamwidth from $90^\circ$ to $30^\circ$ determines a minimal reduction in the SINR outage probability (namely, $4 \cdot 10^{-2}$ at maximum). Also, unlike bi-dimensional mmWave cellular networks, for small BS densities (namely, one BS every $500$ m) it is still possible to achieve an SINR outage probability smaller than $0.2$.