We propose a finite element method for the solution of viscous incompressible flow problems with singular forces at immersed interfaces. The method combines the Algebraic Subgrid Scale method with a pressure jump stabilization. It consists of the addition, to the continuity equation, of a term weighting the residual of the pressure jump. This term enhances the stability irrespective of possible badly-shaped intersections of the interface with the finite elements. We assess the new method by comparing with the unstabilized case showing improved accuracy and robustness. The examples consider immersed actuator disk problems and one application to thermocapillary convection.