This paper analyses the performance of reconfigurable intelligent surface (RIS)-assisted device-to-device (D2D) communication systems, focusing on addressing co-channel interference, a prevalent issue due to the frequency reuse of sidelink in the underlay in-band D2D communications. In contrast to previous studies that either neglect interference or consider it only at the user, our research investigates a performance analysis in terms of outage probability (OP) for RIS-assisted D2D communication systems considering the presence of interference at both the user and the RIS. More specifically, we introduce a novel integral-form expression for an exact analysis of OP. Additionally, we present a new accurate approximation expression for OP, using the gamma distributions to approximate the fading of both desired and interference links, thereby yielding a closed-form expression. Nevertheless, both derived expressions, i.e., the exact integral-form and the approximate closed-form, contain special functions, such as Meijer's G-function and the parabolic cylinder function, which complicate real-time OP analysis. To circumvent this, we employ a deep neural network (DNN) for real-time OP prediction, trained with data generated by the exact expression. Moreover, we present a tight upper bound that quantifies the impact of interference on achievable diversity order and coding gain. We validate the derived expressions through Monte Carlo simulations. Our analysis reveals that while interference does not affect the system's diversity order, it significantly degrades the performance by reducing the coding gain. The results further demonstrate that increasing the number of RIS's reflecting elements is an effective strategy to mitigate the adverse effects of the interference on the system performance.