No saving your back here. Doing like you have mentioned will create one heck of a garden by the lasagna method but not a driveway.

The grass will just grow through the membrane and gravel eventually and quickly. It will also rot in place and when it rains you will have a boggy mess when you stand on it. You certainly could not park a car on it!

Over time it will sink and sag and just look a mess because that is not a proper base for a driveway. A good try , but sorry, no.

also without digging out room for the 2" to 3" you need will involve elbow grease but realy a big failing with ive found with membrane and a mulch is the worms tend to put dirt on top and things drop in there including seeds and you actualy get life all above it and thats without actualy driving or walking on it as it dends to get ruts in it and get kicked and walked about and stuck in your car tires . you can do some crackin car drives with cement with todays materials , the internert like this site . you can even leave bits out fo growing some specialist plants in it . youl look at this in 2 years and be much more unhappy if i learnt anything in gardening and infact life is to do it right the first time . its false econamy keep redoing your drive every 2 years when you can get it done just as you want it with a one of payment for basicly life with the right qualifacations who know what there doing .sorry about that but its better to know the truthe now rather than later .

Noseypotter is absolutely right! With regards to time, effort and cost; A MISER DOES THINGS TWICE.