When your mother is paying for the party, she should be listed as the host. At the party you can publicly thank the friend for offering his home. After the party you may want to send him a gift certificate or something along with a thank you note.
Syringa is right, you should acknowledge whoever is hosting as the person who is paying on the invite. Simply offer your friend a gift to show your appreciation or take them out for lunch/dinner. Thanking them in a speech would also be a nice touch!