LoveFilm plans to use the partnerships to raise awareness of its brand and to increase online rentals.
The partnership with Burton involves rewarding customers who spend on their storecard during December with two free cinema tickets and a free 30-day trial of LoveFilm.
It will be promoted through the Burton storecard, website and email newsletter.
The partnership with National Geographic Channel will give every member of its Viewers Club two free cinema tickets and a free 30-day trial. It will be promoted through National Geographic's magazine, newsletters and on its website.
Metro readers will also gain the same rewards when they pick up a copy of the free paper during December. The promotion will be featured on a series of half pages in the newspaper, on email newsletters and on the Metro website.
Paul Greenwood, partnership marketing manager for LoveFilm, said: "Partnership marketing is a highly cost effective way to drive online rentals while raising awareness of the LoveFilm brand to several key target audiences through these lifestyle focused partnerships that provide the perfect environment to target potential customers."