Tsunamis are devastating natural phenomena that cause extensive damage to both human life and infrastructure. To mitigate such impacts, tsunami early warning systems have been deployed globally. South Korea has also initiated a project to install a tsunami warning system to monitor its surrounding seas. To ensure reliable warning decisions, various types of data must be combined, but efficiently transmitting heterogeneous data poses a challenge due to the unique characteristics of underwater acoustic communication. Therefore, this paper proposes a Hybrid Duplex Medium Access Control (HDMAC) protocol designed for a tsunami warning system, with a specific focus on heterogeneous data transmission. HDMAC efficiently handles both seismic and environmental data by utilizing hybrid duplexing, which combines frequency duplex for seismic data with time duplex for environmental data. The protocol addresses the distinct transmission requirements for each data type by optimizing channel utilization through a group Automatic Repeat request (ARQ) scheme and packet size adjustment. Theoretical analysis predicts that HDMAC can achieve a channel utilization of up to 0.91 in smaller networks and 0.64 in larger networks. HDMAC is validated through simulations, and the simulation results closely match these predictions. The simulation results demonstrate the efficiency of HDMAC in supporting real-time submarine earthquake monitoring systems.