Eminem's latest music video for the single "Houdini" is out, and among the millions viewing the banger is the family of the OG Batman Adam West, who loved the rapper's salute to his work.

In the video for the track, which is part of Em's upcoming "The Death of Slim Shady" LP -- he's back in the ol' Robin outfit he was wearing back in 2002 .... when “Without Me” rocketed to No. 1 on the charts.

Nina Tooley, West's daughter, told TMZ her dad would have loved the video, which in the family's opinion spoke to the enduring brilliance of the TV show and her father's version of the Caped Crusader.

Nina said while she was watching Eminem's new video, she could hear her dad's distinct chuckle when the rapper was trying to scale a building with the Bat Rope ... just like West and costar Burt Ward did in the series.

While the West clan's digging the video, the song's lyrics are pretty biting -- Eminem didn't spare anyone's feelings, going after Dr. Dre, his own kids and Megan Thee Stallion ... in his tongue-in-cheek way, of course.

Tons of cameos are stuffed into the video -- Snoop Dogg, 50 Cent, The Alchemist, Pete Davidson and Shane Gillis ... all of whom contribute to the superhero craziness, as do his kids Alaina, newly-married Hailie Jade and Stevie.