There are no rules on the books IRT service couples serving on the same mission. In fact, having the CoC stopping you from going over because of your spouse going is not a smart thing for them to do. HSS always has someone going over whose spouse is there too, and occasionally even in a diffrent section of HSS coy (I personally disagree, but again, not my decision)
The people that may stop you from going over are the padre and mental health. One question you will have to address is how functional you will be if the other is injured or killed while both you are there. If you have children, ensure you have good support in place, or they will recommend one of you not going over.
In the end, based on their recommendations it will come to a CO's decision whether to let you both go. I have only heard of one case where they did not let one of the service spouses go over, because of child care issues. (personally, if you have preteen children, you are insane to both go over at the same time.)
In your case, EMEgirl, it would depend on your specific units sending you at the same time, but there should not be a problem.
Of course, as mentioned, as officers, the fraternization rules are more strictly enforced as leading by example is important.