general rule of thumb... don't dip your pen in the company ink
That being said, as a midi at a NROTC unit you are not subject to the UCMJ unless you are on summer cruise. The unit CO may discourage it, but if you are professional about it and keep it from becoming an issue, there is nothing really that can prevent you from dating another mid. Believe me, it was not uncommon.
Again though, don't sh!t where you eat! plenty of other girls at a big school.