As long legs are AZ coded but MH operated and MH is not (and never be) in ST, I do not think you can earn miles on other ST partners, even if they are MH partners.

http://www.flyertalk.com/forum/16583960-post17.html
It is a specific example but I think it is alliance-wide.

You need to look on the partner page of your FFP. It is stated to credit mileage on a ST flight, it should be ST operated.
IMHO, I would stick with MilleMiglia.

You also need to look at your booking class as all fares do not credit 100% of the mileage.