The main contribution of this paper consists in integrating a physically correlated shadowing model of the aggregate interference in a stochastic geometry-based approach. The considered shadowing takes place in a Manhattan urban grid and combines both penetration and corner diffraction when modeling signal transmission from base stations to users. A tractable expression for the network coverage probability is obtained thanks to the framework of stochastic geometry. Our results suggest that the diffracted mechanisms are dominant compared to building penetration. It is also shown that the second order diffracted signal have little impact on the coverage compared to the first order signals.