Surface which is free or exposed to air with balance of force to maintain it so. If you go by this simple definition, then both liquid and solid have only one free surface. Therefore, we need to expand this definition in terms of force.
Solids have infinite no of surfaces because it has infinite no of shapes and molecules are closely packed to each other and are not able to flow like fluids .for example a brick is made up of mud and this mud is made up of small particles like dry dirt and some amount of water . When masonry makes brick ,by which we can initiate the building design .This small brick will convert into big building with infinite no of surfaces.
Liquids only flow by nature and can change their shape according to the surface . that is why we can conclude it with one surface because our naked eyes will never see the actual behavior of molecules of liquids