I've used Feeder::HelperRole::Mail from dakkars RSS-to-mail program to send me HTML pages with pictures in them. But that module is GPLv3, so taking it verbatim would make your whole program GPLv3, which is inconvenient.

Maybe you can ask dakkar to give you a version of sub entry_to_mime that has a more liberal license. In the end, the module does a second pass over already rendered HTML and replaces all <img src="..."> by fetching the referenced URLs and then replacing the tags by <img src="cid:..." and appending the images to the MIME body.