We have used a soft-x-ray laser interferometer to study the collision and subsequent interaction of counterstreaming high-density plasmas. The measured density profiles show the evolution of the colliding plasmas from interpenetration, when the low-density edge of the plasmas first collide, to stagnation at the symmetry plane with density building at the symmetry plane. We compare the measured profiles with density profiles calculated by the radiation hydrodynamic code LASNEX, which predicts plasma stagnation as soon as the plasmas collide, and a particle-in-cell code, which allows for interpenetration, softening the stagnation.