There is common ground between your music and theirs - guaranteed. But if you want to encourage some crossover interest, you've got to find that common ground and play it up, cause they're perfectly happy with the way things are.

So what do you like about classical music?

Is it the grand romantic sweep of Beethoven?
Is it the poppy, catchy tunes you can whistle, like Mozart?
Is it all the complex, overtly intellectual Baroque stuff, lots of little embroidery going on in the background?

Or what kind of music do they like, and what do they like about it? Dig beyond "it's cool"/"it's just noise" and look for musical similarities.

Get them to recommend some music that they think might possibly suit you, and give it a listen. Even if it doesn't, it might be slightly more tolerable for you to listen to while you try to suss out the musical influences and similarities.... Try to compare it mostly to 20th-century classical composers. You're much more likely to find echoes of Mahler in your kids' music than shades of Palestrina. Not that the Palestrina isn't ultimately there but it's not going to be as direct or obvious.

Next pick a band of theirs, find out who the major influences were - and who influenced those bands, and so on. Listen to all of it. Eventually you'll get to the Beatles (practically guaranteed), and then brass band music, and - well, that's almost classical, isn't it?

Essentially I guess I'm suggesting a DIY music appreciation course aimed at really understanding the link between their music and yours, instead of just positing that one exists. If you don't understand it you are not gonna be able to make them see it either.
If that sounds too much like work go and read some of Alex Ross's stuff, e.g. the collection of essays "Listen to This" - and then listen to some of it.