Full-duplex (FD) transmissions have emerged as a spectrally efficient technology with the evolution of enhanced self-interference (SI) suppression techniques. However, the FD transmission mode (TM) may not consistently outperform the half-duplex (HD) TM due to the residual SI. In contrast, an adaptive FD/HD transmission scheme utilizes the advantages of both FD and HD TM. This paper proposes an adaptive FD/HD transmission scheme for a cooperative device-to-device (C-D2D) communications system wherein cellular uplink data is relayed through a D2D transmitter (DT). Additionally, a joint DT and TM selection algorithm is introduced to identify the best relay and favorable TM for the multiuser C-D2D system. Further, a probabilistic mathematical framework is developed to evaluate the proposed adaptive FD/HD transmission scheme. The analytical expressions of D2D and cellular outage probability for each TM (FD/HD) have been derived. Results show that FD TM performs better than HD TM when a maximum of two D2D users mapped to a cellular user. However, a trade-off between FD and HD TM is observed for a large number of D2D users. Specifically, when the cellular outage constraint is low, HD TM performs better than FD TM, whereas FD TM outperforms HD TM for high cellular outage constraint.