Device-to-device (D2D) communications in cellular systems have been envisioned as a promising technique to compensate for spectrum scarcity. In this paper, we analyze the performance of overlay D2D communications in two-way cellular systems by employing a three-phase hybrid decode-amplify-forward (3P-HDAF) relaying scheme. Herein, two D2D users provide relay cooperation to the bidirectional cellular transmissions to support certain target rates with the opportunity of sharing same cellular spectrum for their own information exchange. With the proposed 3P-HDAF scheme, one complete round of end-to-end information exchange for both cellular and D2D systems can be accomplished in three time phases, wherein the D2D users can adaptively select either decode-forward or amplify-forward relaying strategy to facilitate the cellular transmissions. For performance analysis of considered setup, we derive the expressions for outage probability (OP) of both cellular and D2D systems by posing asymmetric traffic requirements under Nakagami- m fading. Further, to gain better insights, we obtain the asymptotic OP expressions in a high signal-to-noise ratio (SNR) regime. Hereafter, we deduce some key design parameters such as the critical value of power splitting factor and spectrum sharing region. Moreover, we also obtain an expression of average system throughput to conduct a fair performance comparison with similar existing schemes.