Back in Canuckistan, I used to date (and later shacked up with) a girl from the same unit, and we kept things discrete as possible when working, its not that difficult.
Ya, like all guys, I was a frat rat to a degree, you know, summer flings at Dundurn, same rank stuff, in the mess out to Saskatoon for a dirty wknd stuff, but around in uniform, etc, we always kept our distance. We feared the worst of course, maybe an RTU and the embarrassment that would cause not only to you, but your unit.
Seen lots of both discrete frat, and in your face stuff over the years, more so in the CF than here, but I dated a UCC/PTI here in Aussie back just after I was separated from Ex wife No1 (hey there is only one Ex wife). We went out for 2 yrs, and we kept that quiet and low level, although it was common knowledge. It did cause some problems for her, as she was, yes, hot and blonde, and would cop it from her peers and others (about 'her lumberjack' :

), which she hated. I told her if she was fat and ugly, she wouldn'y get all the attention.
Whats this thing with blondes anyways?
On a more serious note, you just gotta be professional about it. Was I? Well, most of the time anyways.
Cheers,
Wes