Assume it's not hard for them to pronounce, if perhaps they are from a different nationality?
I think as you don't know them well or see them directly for a conversation, your DH should have a proper talk with them. Not just "not Jess, it's Jessica" but more like:
"Mum, dad, I want to talk to you about an important thing that I need your help with. Thank you for welcoming Jessica in x and Y way. It means a lot to me. But there's one thing that hasn't been right and is spoiling the interaction, I've noticed you always call Jessica Jess. unfortunately that's really upsetting her and me. Everybody in her life including her closest loved ones call her Jessica, so she does not think of herself as Jess. It's also close to my ex's name, so it's really not a nice feeling.
You calling her Jess makes us both feel you aren't listening and aren't accepting her. And that's hurting our feelings. I want you to have a close relationship with her, and this is creating a barrier.
So, I'm asking you to make a big effort and use the right name for her. She and I will be very grateful and it will take away this barrier to you getting close to each other."
"Now I know it's hard to break a habit/ maybe it's harder to say.... so let's practice now/ do you want to check the pronunciation etc now?"
"Thanks very much for doing this. It would be such a shame for such a simple thing to spoil the relationship, so I will correct you any time you forget so that you can break the habit. And please make sure you use the right name with your friends so that they all know. "