UCLA has their own student organization partners with the San Fernando Valley HfH and builds every Saturday in the Pacioma, CA site. Become a member of the UCLA club and it's a great deal because outside groups usually "donate" about $2000 in order to have their people build. It's a one-time fee!
For an international experience, every year UCLA HfH take two groups of chosen applicants to Peru and El Salvador to build for about 10 days during Winter Break. The application process is competitive and starts in the Spring! You have to provide your own funding, but depending on the efforts of your fellow participants you can organize fundraisers.
Global Village partners with Fuller Center for Housing - founded by the same founder as Habitat for Humanity. The Fuller Center does have religious influences, but no where on the trip was there any proselytizing or anything of the sort, it is very welcoming.
They also have similar domestic opportunities in Florida and New Orleans during Spring Break!