The performance of downlink massive multiple-input-multiple-output networks with co-channel device-to-device communications is investigated in this paper. Specifically, we consider a cellular network with sufficient number of antennas at the base station and typical hexagonal cell coverage, where the cell users and device-to-device transmitters are randomly and uniformly distributed. To obtain the analytical expressions of system-level performance, the asymptotic signal-to-interference ratios for both downlink and device-to-device links are first obtained, which depend on the pathloss and small-scale fading of the interference channels. Since these information may not be available at the service base station or device-to-device transmitters, there exists a chance of packet outage. Therefore, we continue to derive the closed-form approximation of the average goodput, which measures the average number of information bits successfully delivered to the receiver. Hence, the system design trade-off between downlink and co-channel device-to-device communications can be investigated analytically. Moreover, the performance region in which the co-channel device-to-device communications could lead to better overall spectral efficiency can be obtained. Finally, it is shown by simulations that the analytical results matches the actual performance very well.