In this paper, we investigate the effect of irrotational, viscous pressure on capillary instability of the interface between two viscous, incompressible, and thermally conducting fluids in a fully saturated porous medium when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface and when there is mass and heat transfer across the interface. The analysis extends our earlier work in which the capillary instability of two viscous and thermally conducting fluids in a fully saturated porous medium was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. We use the Darcy's model, and a quadratic dispersion relation is obtained. It is observed that heat and mass transfer has a stabilizing effect on the stability of the system and this effect enhances in the presence of irrotational viscous pressure.