heavy mulching over perennials?

Is there any danger with heavy mulching over herbacious perenials? I have lots of perenial sunflowers, black eyed susans, bee balm, lavender and other perenials that lose all their above ground vegetation in the winter and I am worried that if I put to much mulch on them I could kill them. Is 3-6"s of wood chip, grass cutting, shredded leaf mix ok? When planting new plants, should I put them shallower in the soil to accomodate for the thicker mulch?

Thanks!

Andy, while I find most perennials are really good at pushing through mulch, I try to keep it fairly thin when I know plants are underneath.
They generally get through, but the stems and leaves are often weak, and while I have no scientific backup, I imagine pushing through heavy mulch could use a lot of stored energy before it makes it to the light.
I've got exceptions of course:
Bulbs, taproots, stolons and tubers have loads of stored energy, so many large flower bulbs, yarrow, garlic, dandelions, Jerusalem artichokes, potatoes and so on get through fine.
(I have a pretty casual definition of perennial, and these are all perennial for me...)
Actually, I dug out all the JAs as they were threatening a coup

Thanks Leila! I have a couple heavily mulched areas in the yard where I have transplanted so many things that when they all die back for the winter and I mulch I get afraid they wont come back!! Also chickens and dogs traffic'ed these area heavy until I fenced them off...the dogs were ok but I worried that the chickens would scratch up all the perenials. I put some perennial maximillion sunflower and blackeyed susan crowns in early march and I'm just holding my breath to see if they come up...but we got our first asparagus yesterday so hopefully the warmer days will coax everything up.