Hi and welcome zzrg!
In the days I had conenction day-to-day with military I never heard that!
However, since 1992 I haven't been around the troops very often.
I have sent an email to a couple of active duty types.

Soon as I hear I'll let you know .... unless someone beats me to it (wouldn't be the first time!)

Edit - 2 hrs later
Contact made from two officers and one NCO and the concensus is : never heard of "militainment" ... probably some knucklehead's idea to try to make something sound official! That's the gist, anyway.

Hope this hasn't burst any pretty balloons?!

BTW, where did you hear it? Or did you say and I glossed over it?