The six-episode show, described as a strong, emotional drama with comedy thrown in, centres on a female sex therapist who works with three couples from varying social backgrounds.
The idea behind the idents is that Mini offers guidance on relationships with a "Mini guide to romance".
One execution opens with a man and a woman pulling up next to a savannah-like field in their Mini. As they get out of the car, the audience sees that the man is dressed in a leopard suit and the woman in a gazelle outfit.
They climb into the field and the man then chases down the woman.
Another execution shows a man leaving a florist with a huge wreath of flowers spelling out what appears to be "happy birthday". As the man swings the wreath into full view to put it into the boot of his Mini, it is seen to spell the word "slapper".
The campaign comprises one 15-second, one ten-second and eight five-second idents. They were written by Dave Cornmell, art directed by Jane Briers and directed by Sam Cadman at Rogue Films.
Between the Sheets was written by Kay Mellor, who also penned the BBC's Playing the Field and Band of Gold, and stars Brenda Blethyn and Sir Norman Wisdom.
The sponsorship, which was negotiated between Mini's media buying agency Vizeum and Granada Enterprises, continues Mini's association with ITV drama programmes. Its sponsorship of ITV's Cold Feet came to an end when the show completed its fifth and final series last year.