Apache authentication : allow public access to a subdirectory
Solution 1:
Shouldn't be a problem with .htaccess, depending on what the host has allowed.
You could try putting a .htaccess in the sub-folder with the following, although overrides will have to be enabled for the directories it's in.
Allow From All
Satisfy Any
Solution 2:
OK, for a path server.com/private/public:
server.com/private/.htaccess
AuthType Basic
AuthName "Private, keep out."
Require...
server.com/private/public/.htaccess
Allow From All
Satisfy Any
The key here is 'Satisfy Any' which ORs the requirements from upstream together. 'Satisfy All' is the default.