Millimeter-wave (mmWave) communication opens up tens of giga-hertz (GHz) spectrum in the mmWave band for use by next-generation wireless systems, thereby solving the problem of spectrum scarcity. Maintaining connectivity stands out to be a key design challenge for mmWave networks deployed in urban regions due to the blockage effect characterizing mmWave propagation. Specifically, mmWave signals can be blocked by buildings and other large urban objects. In this paper, we set out to investigate the blockage effect on the connectivity of mmWave networks in a Manhattan-type urban region modeled using a random regular lattice while base stations (BSs) are Poisson distributed in the plane. In particular, we analyze the connectivity probability that a typical user is within the transmission range of a BS and connected by a line-of-sight. Using random lattice and stochastic geometry theories, different lower bounds on the connectivity probability are derived as functions of the buildings' size and probability of a lattice cell being occupied by a building as well as BS density and transmission range. The asymptotic connectivity probability is also derived for cases of dense buildings. Last, the results are extended to heterogeneous networks. Our study yields closed-form relations between the parameters of the building process and the BS process, providing useful guidelines for practical mmWave network deployment.