Going to Italy, eh?
Officially no DC miles on
Air One metal, even with LH codes. I did hear somewhere that if the particular flight number series was between X and Y, the miles sometimes credit to bmi. Needless to say I can't remember the numbers... sorry.
If you have an LH M&M card - that would be the safest option. Better still, why not ring DC and ask about the number of miles available on the given flight numbers, omitting to mention it is operated by some strange outfit you've never heard of?