The angle-dependent tunnel magnetoresistance (TMR) is studied in double-barrier magnetic tunnel junctions with a central layered antiferromagnet (DB-MTJs-AF). The study utilizes a tight-binding model to compute the transmission function via the non-equilibrium Green’s function method, incorporating Rashba spin–orbit coupling within the layered AF. The results indicate that DB-MTJs-AF exhibit higher TMR compared to those with a central ferromagnet (DB-MTJs-F). This enhancement is attributed to the unique properties of antiferromagnetic materials leading to improved performance in spintronic devices.