Debian – Lighttpd static file server 403 forbidden error

I installed lighttpd on Debian Jessie for serving static files, I have a USB drive mounted at /media/storage, with /media/storage/www as my document root and my lighttpd.conf looks like this:

server.modules = (
    "mod_access",
    "mod_alias",
    "mod_compress",
    "mod_redirect",
#       "mod_rewrite",
)

server.document-root        = "/media/storage/www/"
server.upload-dirs          = ( "/var/cache/lighttpd/uploads" )
server.errorlog             = "/var/log/lighttpd/error.log"
server.pid-file             = "/var/run/lighttpd.pid"
server.username             = "www-data"
server.groupname            = "www-data"
server.port                 = 80


index-file.names            = ( "index.php", "index.html", "index.lighttpd.html" )
url.access-deny             = ( "~", ".inc" )
static-file.exclude-extensions = ( ".php", ".pl", ".fcgi" )

compress.cache-dir          = "/var/cache/lighttpd/compress/"
compress.filetype           = ( "application/javascript", "text/css", "text/html", "text/plain" )

# default listening port for IPv6 falls back to the IPv4 port
include_shell "/usr/share/lighttpd/use-ipv6.pl " + server.port
include_shell "/usr/share/lighttpd/create-mime.assign.pl"
include_shell "/usr/share/lighttpd/include-conf-enabled.pl"

I want to be able to edit the website with my normal user "jurre".
So I did "sudo chown jurre:www-data /media/storage/www" and
"sudo chmod 740 /media/storage/www" (so I can read, write and execute files, but the web server can only read). Of course I logged out and back in again and then restarted lighttpd after this. I added a simple index.html with "Hello World!" to test the setup, but I keep getting a 403 forbidden error when surfing to

ls -l in /media/storage/www :

total 8
-rw-r--r-- 1 jurre www-data 58 May 16 16:43 index.html

I have also checked the lighttpd error log, but it only shows when the web server was shutdown and started again, no errors whatsoever in the log.