This paper presents the formulation of finite element methods for the numerical modeling of a poro-elastic two-phase (aggregates/mixture phase) solid. The displacement and pressure fields are decomposed, following the EAS method, into a regular part and an enhanced part. This leads to discontinuous strain and pressure gradient fields allowing to capture the jump in mechanical and hydrical properties passing through the interface between the aggregates and the mixture phase. All these enhanced fields are treated in the context of the Embedded Finite Element Method through a local enhancement of the finite element interpolations as these jumps appear. The local character of these interpolations lead after a static condensation of the enhanced fields to a problem exhibiting the same structure as common poro-elastic finite element models, but incorporating now the mechanical and hydrical properties of a two-phase solid.