FB,
All deer and infact all mammals have the membrane you mention. The skin is there to protect the muscle underneath as well as give insulation, protect from infection etc. Muntjac have evolved in such a way that the skin and membrane is very thick and tight ( especialy around the neck and shoulders) so to give protection when the deer is forcing its way through thick bramble and cover. A loose skin would lead to tears.
Skinning is a simple matter of cutting through the skin on the inside of the back legs all the way up to the hocks. Peel the skin back around the haunches and down to the tail. Cut through the tail.
With the beast hanging simply pull the hide down towards the neck. Once at the shoulders I cut the skin off and remove the shoulders and feed to my dogs!
A I shoot so many I dont bother with the shoulders but you could do the same with the fore quater as with the hind quater and free the legs etc pulling the hide of at the neck.
I belive all deer should be hung in the larder with the skin on. This helps prevent dehydration and gives a bit of protection against possible cross contamination.