I had a jetBlue/Etihad connection last week with a similar long layover in JFK. jetBlue checked my bags all the way through, and I could leave JFK and head into the city for the day with only my carry-on. Unlike what sfozrhfco said, I did not have to go to Terminal 4 to drop my checked bags.
It should be the same for you on Emirates. If jetBlue's self check-in machines at DEN do not show MXP as your final destination, speak to a check-in agent and they will check them all the way for you.
Also, just for your information, JFK has a luggage storage facility in Terminal 4's arrival area. You should not have to use this.