The federal government and most states have laws which make it a crime to record phone conversations without the consent of at least one party to the conversation. In some states (such as California), the consent of all parties to the conversation is required.

In other states, only one party needs to give consent. In any case, information obtained from an illegal recording will not be admissible in court. However, if the recording is made in accordance with the law, it will usually be admissible in court.

If the conversation is between a spouse and a third party, it is very unlikely that any recording of this conversation will be legal, since it is unlikely that either party (let alone both) have consented to have the conversation recorded. 

Under federal law, and the majority of states, there is no exception to these laws when one spouse is recording the other.