In this paper, we propose and investigate a three‐phase overlay spectrum‐sharing scheme for device‐to‐device (D2D) communications in a bidirectional cellular network with nodes mobility. In this scheme, a pair of D2D users facilitates relaying to the cellular nodes (base station and mobile user), and in return, they get the opportunity to exchange their own information by exploiting the same cellular spectrum. With this, the two end‐to‐end bidirectional communications (D2D and cellular) can be realized in three time phases by using selection‐combining technique at both cellular nodes and decode‐and‐forward (DF) relaying scheme at both participating D2D users. For DF operation, we consider two strategies, namely, exclusive‐OR (XOR)‐based DF, and superposition‐based DF. All the channels are assumed to be time varying, and Markovian model is used to characterize the impact of nodes mobility. For this set‐up, we first derive the outage probability for both cellular and D2D links under Rayleigh fading. Then, we obtain the asymptotic expressions of outage probability for both systems and used them further to reveal the critical value of power‐splitting factor for spectrum sharing. Above all, we acquire the expression of average system throughput to perform a fair performance comparison with the other existing schemes.