What actually causes spell interrupt now?
 

Since push is no longer a thing, but mobs can still be interrupted sometimes, what is the mechanic now that causes spells to sometimes be interrupted? Just a small chance per hit vs their channeling skill?

Physical bashes and stuns from spells, mana drains.

I'm curious to know this too. (Aside from the obvious answer above.)

Yes, casters can be interrupted just by getting hit with melee attacks. That is why players get the channeling skill. High level mobs are going to be very resilient to this form of interrupt to the point you may rarely see it.

As a solo monk you are better off relying on stun procs than you are melee interrupt.

Slam