This paper studies the benefits of incorporating underlaid full-duplex (FD) device-to-device (D2D) communications into massive multiple-input-multiple-output (MIMO) downlink systems. Due to the nature of cellular downlink and FD D2D transmission, the performances of cellular and D2D services are severely impaired due to high interference caused by base-stations (BSs) and D2D transceivers. As a consequence, integrating a large number of D2D links into exiting cellular networks might degrade the system performances. To overcome this challenge, utilizing the large uniform linear array (ULA) equipped at BSs, we propose a joint beamforming and power allocation design for average sum-rate maximization while considering the effects of interference to both cellular and D2D transmission. The problem formulation leads to a nonconvex vector-variable optimization problem, where we develop an efficient solution using a fractional programming (FP) based approach. Numerical results show that, at sufficiently high self-interference cancellation (SIC) levels and numbers of active D2D links, the FD D2D transmission provides a significant sum-rate improvement as compared to the half-duplex (HD) counterpart and pure cellular systems in absence of D2D.