If both the materials on a boundary are dielectric then do surface charge exists. I was solving using pillbox it showed that there should be surface charge on boundary to satisfy change in normal component of Electric flux density vector. But I am confused how so can happen.
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Dielectric materials have electrons that can move. They do not get ripped out of their orbits which keep the material together (as long as no flames nor smoke occurs) but the orbits get stretched and the amount of stretching changes along the electric field. That makes the permittivity higher than vacuum permittivity. The phenomenon is called "dielectric polarization"
Changing field causes AC current to exist in the dielectric material.The reflected wave can be considered starting from that current.
About surface charge: It can well exist if the wave propagation direction is not perpendicular against the surface - a normal component of E-vector against the surface can exist depending on the wave polarization.