you are right that combined interosseus and lumbrical action is needed for the motion you describe--flexion at the MCP and extension at the IP joints.
spreading and contracting the fingers is exclusively done by the interossei.
the flexors originate in the forearm, near the elbow, and insert either on the distal phalanx ("finger tip") for the deep layer, or the middle phalanx for the superficial layer.
the extensors also originate near the wrist and insert broadly across the fingers.
to flex the fingers while keeping the wrist straight requires input from the extensors, and vice-versa. (to prove this, try gripping something as tightly as possible with your wrist neutral, flexed, or extended, and then feel which parts of your arm tighten)
of course, there's also the various intrinsic muscles of the thumb and 5th finger, as well as a few minor ones of the 2nd finger, but no need to get into those now. and there's the flexor and extensor carpi muscles which act to move the wrist.
the point is, there's a lot of different little muscles that act in concert to produce very complicated movements, and without any of them, you will have trouble doing something like playing a musical instrument (or writing, or typing, or whatever). consider carpal tunnel syndrome: only the intrinsic muscles of the thumb are weakened, yet the effects on a musician are profound.
for a far more detailed look at what I just explained, try Moore and Agur's Essential Clinical Anatomy.