Adultery can be hard to prove, but not necessarily as hard as some imply. There is no requirement that there be an eyewitness or a confession. There just has to be enough evidence to convince someone, your CO in case of NJP or perhaps a jury in case of a court martial. Circumstantial evidence can do it, though naturally more is preferred.
If your alleged co-adulterer decides to testify against you, naturally that will be extemely persuasive evidence.
Of course, you may have complicated things by probably having perjured yourself or making false statements. If you have talked to the other party about it, then there may be obstruction, etc. involved. This means there may be more charges against you, which might convince prosecutors to be more aggressive in pursuit. Many times adultery will be dropped and you'll simply be charged with a related, more easily proven, crime like fraternization or obstruction or violating a no-contact order.
Finally, you want to be very nice to your wife. "When one spouse is charged with adultery, the marital privilege does not apply to communications inolving the adultery" (United States v. Taylor, a January case from the Navy/Marine court of military appeals). I doubt you want your wife on the stand testifying "My husband admitted he did it..."
You should get a lawyer. If, for example, you contacted your lover and told/urged them to deny anything happened -- then you may be open for obstruction charges and might want to consider pleading to adultery in order to avoid more charges. Likewise, if you have made false statements (not just about adultery per se, but about times you visited your partner, etc.) then you may also be liable for more charges. You don't have to make self-incriminating statements, you can refuse to answer questions. But the instant you DO answer, if you lie, then you are opening yourself up to a whole new array of charges. Often, by the time a lawyer is consulted, their client has already obstructed and given false statements. It is often a judgement call as to how to proceed.