The motto of Fort Carson’s 10th Combat Support Hospital is “IN CRUCE VINCAM” which translates to “I Shall Conquer By The Cross”. And the CSH’s distinctive unit insignia has two *gasp!* crosses on it (one maroon and one white). That would really make their heads explode!
http://www.tioh.hqda.pentagon.mil/Heraldry/ArmyDUISSICOA/ArmyHeraldryUnit.aspx?u=4766
That is absolutely fascinating. I'm sure there's a martial aspect to it, but the faith aspect is that by Christ's sacrifice on the cross, we have received forgiveness of our sins and the promise of everlasting life - thus conquering sin and death.
If I remember correctly the red cross represents caring for those hurt during war while the white cross symbolizes caring for those hurt during times of peace.