In fluid-structure interaction (FSI) simulations, the interface between the fluid and the structure is a discontinuous region of the materials, where connection of the fluid and the structure should be done in a consistent manner. For the formulation of this interaction term in the context of SPH, various schemes have been proposed, such as the Fluid-Structure Acceleration-based (FSA) coupling scheme by Khayyer et al. [1] and the Pressure Integration (PI) coupling scheme by Antoci et al. [2]. However, in the conventional methods, without an additional artificial stabilisation term, numerical noise may arise in the calculation results of physical quantities such as the pressure field in the vicinity of the interface or at the interface, which may have a negative effect on the entire system response. Therefore, in this study, a novel FSI coupling scheme with a Riemann-based stabilisation term is proposed to ensure stability and, more importantly, to enable physically consistent transfer of momentum from the fluid to the structure and vice versa, targeting the ISPH-TLSPH coupled solver that employs ISPH for the fluid and TLSPH for the structure. The TLSPH structural model employs the recently proposed C2nd (second-order Consistent) and cR (complete Riemann) schemes to accurately and stably simulate non-linear and finite strain elastic structural responses. Furthermore, a reformulated VEM (Velocity Divergence Error Mitigating) scheme [3, 4] is presented for interfaces to ensure further stabilisation related to the kinematic discontinuity at the interface. Benchmark tests show that with the proposed Riemann-based fluid-structure interaction term incorporated together with VEM for interfaces, the calculated fields around the fluid-structure interface are stabilised and more physically consistent results are obtained. The detailed results will be presented during the PARTICLES 2025.