Reconfigurable intelligent surfaces (RISs) have shown the potential to improve signal-to-interference-plus-noise ratio (SINR) related coverage, especially at high-frequency communications. However, assessing electromagnetic field exposure (EMFE) and establishing EMFE regulations in RIS-assisted large-scale networks remain open issues. This paper proposes a stochastic geometry (SG) based framework to characterize SINR and EMFE in such networks for downlink and uplink scenarios. Particularly, we carefully consider the association rule with the presence of RISs, accurate antenna pattern at base stations (BSs), fading model, and power control mechanism at mobile devices in the system model. Under the proposed framework, we derive the marginal and joint distributions of SINR and EMFE in downlink and uplink, respectively. The first moment of EMFE is also provided. Additionally, we design the compliance distance (CD) between a BS/RIS and a user to comply with the EMFE regulations. To facilitate efficient identification, we further provide approximate closed-form expressions for CDs. From numerical results of the marginal distributions, we find that in the downlink scenario, deploying RISs may not always be beneficial, as the improved SINR comes at the cost of increased EMFE. However, in the uplink scenario, RIS deployment is promising to enhance coverage while still maintaining EMFE compliance. By simultaneously evaluating coverage and compliance metrics through joint distributions, we demonstrate the feasibility of RISs in improving uplink and downlink performance. Insights from this framework can contribute to establishing EMFE guidelines and achieving a balance between coverage and compliance when deploying RISs.