Blacktown City Council - Nature Strip Policy
This policy has been in place for some years. It's not particularly encouraging but if you follow the guidelines, you should be able to plant a native nature strip.
"It is Council’s preference for vegetated road verges and nature strips to remain predominantly grass or turf species with a street tree planted in the vegetated road verge. However, should the resident wish to convert their vegetated road verge from grass to a low shrub garden bed or to synthetic grass, these requests must be made in accordance with criteria on pages 7 & 8 and application forms on page 20 within this policy."
"Works are NOT to commence on the modification of nature strip areas without the written consent of Council."
See details at www.blacktown.nsw.gov.au/Services/Tree-management/Trees-on-public-land and click on the Nature Strips tab and follow the links