There will not be separate billets, the DoD has made it clear it follow the recommendations of the "Report of the Comprehensive Review of the Issues Associated with a Repeal of “Don’t Ask, Don’t Tell.” Otherwise known as the DADT survey. Pages 12, 13, 14, and 141 will show you exactly how the military will handle the issues of billeting and seperate shower areas, on page 12 where at the bottom under a subsection called Privacy and Cohabitation it reads:
http://www.defense.gov/home/features/2010/0610_gatesdadt/DADTReport_FINAL_20101130(secure-hires).pdf
Now that is only an assessment, but I think you'd agree its very accurate. You and I both know how difficult it can be sometimes to secure private areas for men and women, and I don't think either us would disagree that making a 3rd or 4th category is practical in the least.
As far as sexual harassment due the presence of gays the report has this to say:
Now what I expect is a comparably smooth transition in comparison the end of racial segregation and the introduction of women into the regular service, and their continued increased pretense throughout the service. That is because, as the survey showed, many of the US military knows someone who is gay within their unit. So many servicemen are already serving with what are all for practical purposes openly gay individuals. Also unlike when racial or gender segregation ended, there will no new introductions into a unit. A man, who is uncomfortable with gays to one degree or another, who suddenly discovers his buddy is gay, is less likely to cause problems about it. Why? Because he knows his buddy, they have a history and a trust built up over time, unlike a racist for example who suddenly comes into work one day and finds several black Soldiers, whose he never met before and has no relationship with, in his office or unit.
Post-DADT: Racial, sexual integration are guide - Army News | News from Afghanistan & Iraq - Army Times
Of course it won't be entirely smooth sailing there will be incidents of sexual discrimination, crimes motivated by Soldiers who now see a homosexual in their ranks, and issues of some people leaving the military which will no doubt include a few unquestionably highly valuable Soldiers.
What I do NOT expect to see is a massive rise in sexual harassment as you predict, specifically because gays are already serving in our military and are being much smaller in number than women or blacks, at least according to the survey's estimates. The survey estimates there are roughly 46,000 homosexuals currently serving in uniform. Now I don't know how many sexual harassment incidents there are a year but I do know that there is no way 46,000 people can commit double or triple the amount of sexual harassment seen in the military. A gay rights groups has an estimate of 66,000 in active duty, or roughly 2% of the total.
Federal Eye - Eye Opener: Estimate: 66,000 gays in the military
So you are suggesting that 66,000 people will have double or triple the amount of sexual embarrassments as the roughly 833,000 active duty service members. That means you are suggesting that for every act of sexual harassment committed by a straight service-member, 12.5 homosexuals will commit an act. And thats to keep the numbers even between the two groups. To double, 25 homosexuals will commit an act of sexual harassment for every one straight Soldier, 37.5 for triple. That by the way is a 1250% higher rate of sexual harassment for homosexuals to say even, 2500% higher to double, and 3750% higher to triple.
If we assume that 10,000 acts are committed every year, that means of those 66,000 gay Soldiers, 125,000 will commit an act to stay even, 250,000 to double, and 375000 to triple. In other words you think its plausible that on average each gay Soldier will commit 3 separate acts of reported sexual harassments, since obviously only reported ones go into those rate educations. If we only assume 1,000 are committed every year than we are up to half of all gay Soldiers committed one reported act.