Individual phases of a power are atomic.
In your example, "do 1W+Int damage and push the target 1 square", the damage and push are linked: when the attack impacts you, it both damages you and shoves you simultaneously. An immediate interrupt would take place before both of them, while an immediate reaction would take place after the both of them.
Some powers, however, have fairly obvious "phases", where events take place in sequence, as discussed in this question for example.
As the RC (p92) explains:
The order of entries in a power description is a general guide to the sequence in which the power's effects occur. For instance, an "Effect" entry might appear before an "Attack" entry to show that something happens before the attack.
Thus targeting a creature with an attack is one phase, making the attack roll & determining a hit or miss is one phase, and applying the effects of a hit is one phase; that's why each of these can trigger an immediate action. Some example triggers: "You are the target of a melee attack," "you are hit by a ranged attack," "you take damage".
Consider the barbarian power Hurricane of Blades, PHB2 pg60:
Target: One creature
Attack: Strength vs. AC
Hit: 1W + Strength modifier damage
Effect: Make the attack five more times against the same target or different ones.
Each attack is atomic, but the power as a whole is not. Suppose Barbarian Bob uses Hurricane of Blades while fighting a single enemy. If that enemy uses an Immediate Reaction power that triggers on taking damage after the first attack to teleport away, the remaining 5 attacks are wasted. The reaction takes place after the first attack resolves, not after the entire power resolves.
Note that movement is never atomic: each square moved is an individual event.
From the RC, pg196 (emphasis mine):
Likewise, an immediate reaction can interrupt movement. Here's how: If a creature triggers an immediate reaction while moving (by coming into range, for instance), the reaction can take place before the creature finishes moving, but after it has moved at least 1 square. In other words, an immediate reaction can be in response to a square of movement, rather than to an entire move action.