BuddyPress.org

WordPress detects the currently enabled theme’s root and css directories via the bloginfo(‘template_directory’) and bloginfo(‘stylesheet_directory’) functions.

To call the css and images from the home theme in a member theme template you would have to hard code the path references as “/wp-content/themes/buddypress-home/styles.css”.

Personally, as hard coding is generally a bad idea, I would suggest simply copying the elements you wish to use from the home theme directory to the member theme directory and reference them the usual way.