While you handled it well and my first step in most circumstances would have been the same, my personality would require one more step.

In a conversational tone, ask to speak with him in private. Huddling in a broom closet isn't required, just step out of earshot. Tell him that joking and kidding is one thing. You're willing to play by big boy rules at work, but making back-handed comments to your wife is off limits.

Of course, I have no idea what the environment is at your place of employment.

And I agree with the last several posters. There isn't a 21 year old on the planet who is indispensable to a business. If he were struck by lightning, they'd have a replacement as or more competent by the end of the week.

The graveyard is full of people who couldn't be replaced.