Multisite Admin area missing styling?

Host: Network Solutions
WordPress: 4.2.2 Multisite

This is a new WP install, with no additional plugins or themes except those that come with WP.

I installed WP, set permalinks, followed all the general instructions on “Create a Network” in preparation. Do the conversion, choosing subdirectories, and replace my .htaccess:

RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [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).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(.*\.php)$ $2 [L]
RewriteRule . index.php [L]

… and my wp-config.php:

define( 'WP_ALLOW_MULTISITE', true );
define('MULTISITE', true);
define('SUBDOMAIN_INSTALL', false);
define('DOMAIN_CURRENT_SITE', 'subdomain.main-domain.org');
define('PATH_CURRENT_SITE', '/');
define('SITE_ID_CURRENT_SITE', 1);
define('BLOG_ID_CURRENT_SITE', 1);

Everything is fine on the main https://subdomain.main-domain.org/ site, but when I create a second blog, under…

https://subdomain.main-domain.org/subsite/

… the admin area at /subsite/wp-admin has no styles. The frontend loads fine. It does this on every new subsite I create.

I’ve googled around, tried adding this in wp-config:

define('ADMIN_COOKIE_PATH', '/');
define('COOKIE_DOMAIN', '');
define('COOKIEPATH', '');
define('SITECOOKIEPATH', '');

No change.

Could it be because there is another WordPress install at https://main-domain.org/ ?

So, in actuality, there are two completely separate WordPress installs:
/htdocs/site/ = https://main-domain.org/ (a WordPress single site, with its htaccess and index.php in /htdocs/ so that https://main-domain.org/ is the site address instead of https://main-domain.org/site/)
/htdocs/subdomain/ = https://subdomain.main-domain.org/ (a WordPress Multisite)

Any assistance? Thanks.