We propose a new cellular network model that captures both deterministic and random aspects of base station deployments. Namely, the base station locations are modeled as the superposition of two independent stationary point processes: a random shifted grid with intensity $λ_g$ and a Poisson point process (PPP) with intensity $λ_p$. Grid and PPP deployments are special cases with $λ_p \to 0$ and $λ_g \to 0$, with actual deployments in between these two extremes, as we demonstrate with deployment data. Assuming that each user is associated with the base station that provides the strongest average received signal power, we obtain the probability that a typical user is associated with either a grid or PPP base station. Assuming Rayleigh fading channels, we derive the expression for the coverage probability of the typical user, resulting in the following observations. First, the association and the coverage probability of the typical user are fully characterized as functions of intensity ratio $ρ_λ= λ_p/λ_g$. Second, the user association is biased towards the base stations located on a grid. Finally, the proposed model predicts the coverage probability of the actual deployment with great accuracy.