This is a topic near and dear to me, as when I purchased my home, 12 years ago, it included a 70' asphalt driveway. My house faces the driveway -- it's oriented sideways to the street, so anyone coming to the main entrance walks up driveway instead of path. Blah. I didn't need all of the drive, either -- the structure at its end is a barn housing poultry, and the double doors don't admit vehicles wider than a wheelbarrow. So, I laid a row of flat granite cobble blocks across the drive at the spot where I wanted it to end, and filled the entire upper area with peastone and flagstone stepstones for footing. I used more cobble blocks to build raised planters, lineing them with landscape fabric and filling them with topsoil and compost. The plants cascade over the edges and make a nice entry to the upper garden. My driveway is on a slight hill, so there is fine drainage -- water just passes under the peastone. You probably could use landscape timbers, riprap or any prepared paver to make raised planting boxes, or lay peastone and set pre-built cedar, redwood or other rot-resistant planters on top. If your driveway is flat, making drainage slow, that might be the best option.

Ground-ivy (Glechoma hederacea) stays green throughout the winter here and is a common lawn weed. You can compare to that. FataMorgana Here is a link that might be useful: Google images - ground ivy

How about Western Australia Bluebells (Sollya heterophylla)? It's an Aussie native that grows low and would probably prevent erosion if you plant enough of it to cover the area well.

One plant I would definitely not recommend is vinca major (nor would I recommend vinca minor, as it is almost as bad). From personal experience, these have both become invasive in our yard. At first they looked lovely sitting all neat in their beds. Then I had difficulty keeping them from growing up trees. When they did they would bore their roots through and into the tree's bark. We have a large yard. I became sick for a couple of years (this was after they started to become difficult) and couldn't get out to do much yard work, and by that time they grew up most trees that are in the yard and weakened and ultimately led to the demise of many of our lovely trees. Also, causing a hefty tree removal bill. It has become a landscaping nightmare to rid these vines from our yard. They are tough and hard to pull by hand. Also, being under other trees and shrubs and near other plants, chemicals are also difficult to use without killing others.