Game identification Playstation alien FPS game in urban setting

Question

I'm trying to find a game I used to play with a friend around ~2008 on a PS2 or PS3.

At first I was almost certain it was in the XCOM universe, but I couldn't find matching screenshots. Here are the details I remember:

• There are multiple (3 or 4 ?) character classes available. We used to play a minigun-wielding one and a laser gun one; I think the latter was supposed to be the medic.
• Missions take place in a modern near-future urban settings: one on a construction site, one in some sort of museum, one in a zoo/park, and one staring in a street where you end up in the subway, I think.
  • Missions involved securing or recovering some stuff while fighting off the aliens in our way.
  • At the beginning of the construction site and the zoo/park missions, we could hear a radio playing a jazzy tune.
• Enemies are mainly some good ol' Grey aliens with different weapons.
  • A major part of them had more of a reptile-like skull and had some light-emitter antenna backpack or something
  • An especially annoying ennemy group had projectile slowly passing through walls in the museum mission.
• There was some sort of "Grey Matter" reward currency you could use to level up your class or unlock new gear.

Answer 1

I finally found it ! The game is Resistance 2 on PS3 !

Here is a video of a coop mission on the Chicago map:

• They start in the street and goes on to the construction yard and into the subway. Also the jazzy tune I was talking about can be heard at 7:34
• We can see the 3 character class : Sharpshooter recording the gameplay, a bunch of laser medic and minigun wielding ones with their force field barriers.
• The Grey aliens ennemies can be seen at the beginning of the video while those I called reptile-like appear later (9:48 for example)
• At the end of the video (13:42), we can see the squad wins "Gray tech"