Competing cellular operators aggressively share infrastructure in many major US markets. If operators also were to share spectrum in next-generation millimeter-wave (mmWave) networks, intra-cellular interference will become correlated with inter-cellular interference. We propose a mathematical framework to model a multi-operator mmWave cellular network with co-located base-stations (BSs). We then characterize the signal-to-interference-plus-noise ratio (SINR) distribution for an arbitrary network and derive its coverage probability. To understand how varying the spatial correlation between different networks affects coverage probability, we derive special results for the two-operator scenario, where we construct the operators' individual networks from a single network via probabilistic coupling. For external validation, we devise a method to quantify and estimate spatial correlation from actual base-station deployments. We compare our two-operator model against an actual macro-cell-dominated network and an actual network primarily comprising distributed-antenna-system (DAS) nodes. Using the actual deployment data to set the parameters of our model, we observe that coverage probabilities for the model and actual deployments not only compare very well to each other, but also match nearly perfectly for the case of the DAS-node-dominated deployment. Another interesting observation is that a network that shares spectrum and infrastructure has a lower rate coverage probability than a network of the same number of BSs that shares neither spectrum nor infrastructure, suggesting that the latter is more suitable for low-rate applications.