I'm not sure how you mean by "without interrupting each other". As far as I am aware It should be possible to use HSERIAL and HI2C together with current PICAXE, but you'll likely have scratchpad management issues with those and the M2.
The M2's multi-tasking capability won't be a universal panacea as it's still a single core processor at heart, can only do one thing at a time, so things that clash with each other on existing PICAXE's won't magically work on the M2.
In the PICAXE software sense multi-tasking will deliver what it promises; take a loop which toggles a LED with a pause and it works, add the same loop again for a different LED and a different pause and it too will work, running (apparently) simultaneously with each other, each LED toggling at its own rate.
For background hardware it's still the same single processor running the show, just as before it cannot do two things simulataneously.