Check with a good accountant for the right strategy.
I'm not an accountant, but--in brief--the equity in your home is an asset. If you didn't do anything else (such as putting the house in a trust), The executor of the estate would have a $200,000 home with a $120,000 debt. Most likely, the executor would sell the home for $200,000, pay off the mortgage, and the equity--the $120,000 would remain in your estate. It then would be divided up as you specified in your will. If you didn't specify a division of assets in your will, then state law takes over (you'd have died intestate), specifying which relatives (children, grandchildren, etc.) receive the proceeds.
However, that's a really messy way to do it. You need to consult with someone who specializes in estate planning. Most likely, the recommendation will be that your home (and possibly other assets as well) be placed in a trust. It's then a lot easier and cleaner to convey those assets to whomever you want.
Hope that helps.