Normally my advice would be to report the issue to the 1SG or commander but when the offense includes either the commander or the 1SG my recommendation is to take the issue straight to the battalion commander. If your sergeant major tries to become involved respectfully decline and request that you be able to see the battalion commander and the battalion CSM at the same time on open door policy immediately.
Once you have their attention, ask that they keep the matter as discreet as possible. Then explain the situation. Provide the facts you have to support your allegations. Try your best not to become emotional or irrational. Your chain of command will take this allegation seriously and take the necessary steps to resolve the problem. If they are having an affair or they are displaying acts that may lead to the perception of an affair you can rest assured your chain of command will deal with the issue quickly. Should your chain of command not take your allegation seriously, report the situation to the IG.
If the offending commander attempts to speak with you respectfully decline. If a conversation is unavoidable try to have a neutral party present. If this is not possible simply listen and do not make any statements. Remain calm and professional.
In all my years of service, these allegations were rare, but when they were reported the issue was addressed swiftly.
It is also important that you and your spouse seek assistance. This is a difficult time for both of you. Take your time so you can work through this issue. Support can be found through several agencies on post. You may also wish to utilize the chaplains office (you may want to see another chaplain outside your brigade to help ensure privacy).