The formation of porous sea ice in the polar oceans is a complex process influenced by the interaction between saline seawater and temperature. As ocean warming and environmental changes continue in these regions, a likely impact on the microstructure of sea ice is expected to occur, which in turn affects the biogeochemical processes associated with ice formation. To better understand and model the phase transition phenomena, this study presents a biphasic model that considers both solid ice and saline seawater within the framework of extended Theory of Porous Media (eTPM). This approach applies a continuum mechanical treatment on multiple phases and components associated with ice and seawater. The model captures phase transition between ice and brine using an interfacial mass transfer method, where the mass exchange is treated as a jump across an interface separating the two phases. This mass production is governed by factors such as heat flux, specific enthalpies, and the interfacial area. The resulting system of equations provides a high-fidelity representation of the ice-brine interactions and is solved using the Finite Element Method (FEM). To validate the approach, the study includes academic test cases as proof of concept.