This looks to be a 'standard' height for a mw/oven and should be fine for most people.

I understand your concern if the door folds down instead of sideways. Have you considered putting it in a base cabinet towards the top? Open area for your mw/oven on top with maybe a big pot & pan drawer below?

I'm thinking of making a stackable cabinet next to fridge, MW at about counter height, drawers below and a cabinet above?

How about something like this? It is so much nicer to have the m/w away from the range/stove. In each of these instances the placement of the m/w is lower for easier access without interfering with ventilation etc.

It's not next to the range or stove. It's between dishwasher and refrigerator. The microwave is also a speed oven and it's a built in so I think I'll need a stackable cabinet?

That should work. You said between d/w and fridge originally and for some reason when I looked at the diagram I was thinking range (brain blip). I personally prefer the lower one with drawers below and cabinet above.

Your refrigerator seems (and usually it is) deeper than the m/w cabinet. If you move the m/w next to the refrigerator, it may not be so easy to use it, and the whole assembly (fridge + m/w) may look too "bulky". The way it shows now on you sketch, it seems standard height, and it also gives you plenty of counter space.