From what I've been reading, it sounds like its still supposed to follow the same format as The Betrayal of Jimmy. The only difference is that the first game takes place before Jimmy gets betrayed by his handlers and the second one is after he gets out of jail and kills them all.

If you haven't played The Betrayal of Jimmy, its an arcade game where there's a cutscene at the beginning and a cutscene at the end. It has all the same options as Mafia 2 when it comes to things to do outside of missions, except they have 2-3 missions active at once like the GTA series with mission markers on the map. When you get to the marker location, there's a little icon that floats on the ground that, when you activate it, a little screen comes up with a screenshot of the boss doing something and about a paragraph explaining what the mission is about. There's no cutscenes for accepting a mission (which I thought would've been pretty cool because then it would have been like playing an entire game).

You can free roam during the game between missions and you can free roam when you finish the game to go back and play the missions you already beat (the floating icons stay on the map and in their locations but in a silver colour showing that you finished it instead of a gold colour).

So, I wouldn't really call it "story missions" like Mafia 2 since its not anywhere near that well-developed. Basically there's a couple different kinds of missions that you get from three different bosses:

1. Car Dealer Missions: always involves driving across the map to pick up a car that may or may not be guarded and then driving it to a garage.

2. Chinese Missions: you work for the Irish who gives you missions to dismantle the Tong. They usually include destroying shops, destroying crates scattered around the map, an assassination mission or two, killing large amounts of Chinese, and then fighting your way through the restaurant in Vito's story and killing the leader of the Tong at the end.

3. Bomber Missions: you work for an Italian named Sal Gravina who gives you missions to dismantle the Bomber gang. Also involves destroying shops, their cars, assassination missions, killing large numbers of Bombers, and fighting through the distillery from Vito's story to kill the leaders of the Bombers.

4. There's two "story missions" which activate at the beginning of the game and at the end once you beat the 28 or so Car Dealer/Chinese/Bomber missions. You start the game in the middle of a mission where you're just killing some random people and drive to a guy's mansion in Highbrook, then the second of three cutscenes take place. Then once you beat all the missions throughout the city, the Irish guy and Sal ask you to go pick up a car filled with money in it for your reward and the last cutscene triggers there.