The demand for vehicular mobile data services has increased exponentially, which necessitates alternative data pipes for vehicular users other than the cellular network and dedicated short-range communication. In this paper, we study the performance of underlaid vehicular device-to-device (V-D2D) communications, where the cellular uplink resources are reused by V-D2D communications, considering the characteristics of the vehicular network. Specifically, we model the considered urban area by a grid-like street layout, with nonhomogeneous distribution of vehicle density. We then propose to employ a joint power control and mode selection scheme for the V-D2D communications. In the scheme, we use channel inversion to control the transmit power, in order to determine transmit power based on path loss rather than instantaneous channel state information (CSI), and avoid severe interference due to excessively large transmit power; the transmission mode is selected based on the biased channel quality, where D2D mode is chosen when the biased D2D link quality is not worse than the cellular uplink quality. Under the proposed scheme, two performance metrics of V-D2D underlaid cellular networks, i.e., signal-to-interference-plus-noise outage probability and link/network throughput, are theoretically analyzed. Simulation results validate our analysis and show the impacts of design parameters on the network performance.