Unable to upload images using Multisite

I’m using the Multisite feature with my blog. I’m able to upload photos fine while posting to the main site. However, I’m unable to upload any media successfully to any of the other network sites. I receive the following error:

“image.jpg” has failed to upload due to an error
Unable to create directory /home/name/name.com/wp-content/blogs.dir/3/files/2011/06. Is its parent directory writable by the server?

I have the permissions set to 777 on both wp-content and blogs.dir.

My .htaccess file looks like this (which is set in the root of my domain):

# BEGIN WordPress
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]

# uploaded files
RewriteRule ^([_0-9a-zA-Z-]+/)?files/(.+) wp-includes/ms-files.php?file=$2 [L]

# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule  ^[_0-9a-zA-Z-]+/(wp-(content|admin|includes).*) $1 [L]
RewriteRule  ^[_0-9a-zA-Z-]+/(.*\.php)$ $1 [L]
RewriteRule . index.php [L]
# END WordPress

Looks like everything should work…but it doesn’t. I wish WordPress was more helpful in their documentation regarding this common problem. Any help that anyone could give would be appreciated.