Peat is already composted, under water, at cold temps. It is pretty sterile and, thus, has nothing left to compost. It works best as a mulch.

The plastic netting has me stumped. Do you have a picture?

Apparently it is just called Plastic netting. Duh. It can be seen in a picture of a roll of sod near the bottom of the page.

Sorry for the late bump on this thread, but I wanted to chime in & tell you to GET RID of ALL of that horrible netting if you can. We have it in our yard- apparently it's a wood-shaving seed mat that's backed with the plastic stuff to help hold it together & in place.
It's a cheap way for contractors to seed & mulch a lawn while skimping on good topsoil. Ours has become exposed in spots all over the place & it wreaks havoc on doggy toenails and especially the lawnmower. If you try to rip it our your lawn will come with it. (good for you, but if you want to KEEP the grass you have to cut the stuff out). Awful, awful stuff.