Plesurf, it sounds as if you have the same kind of liner I have. Mine's edged with turf on two "sides" (it's oval so it doesnt' really have any sides) and has one deep edge with a logpile, and one shallow beach of gravel. It's exposed in places but not excessively. I think yours will be fine as long as you allow the grassy edge to trail down.
Plants that love the pond edge include brooklime (veronica beccabunga) and water dell/creeping jenny, and, as someone above posted, ivy makes a lovely trailing "fringe".
Good luck with your pond!
