First, a minor issue: "Mitra/Mithra" is usually used to refer to the Zoroastrian divine being, while "Mithras" refers to the Roman deity (whose exact connection to the Persian deity is a matter of much debate).

As you said, the mystery cult of Mithras only accepted men. Manfred Clause points out that, while women could not be part of Mithraism, "within the wide range of cults in the Roman Empire there were also some exclusively for women". Isis was one of those, as mentioned by /u/Sleepwaker, though there is no a priori reason to believe that the wife of a Mithraic initiate would necessarily be an initiate in the mysteries of Isis.

Religion wasn't quite the same 'us vs. them' thing it is seen as today. A Mithraic initiate would, almost invariably, also worship the Roman pantheon - as would his wife. For example, one centurion of the legio VIII Augusta set up separate altars to Mithras, Apollo Pythius, and Fortuna Respiciens. There are also many votives to other deities found within mithraea.

So, the Mithraic initiate would have worshiped other gods and his wife likely would have worshiped the same gods as her husband, simply minus Mithras.

Mithra and Isis were two prominent characters during a period of Roman religious reformation in the first century. The predominant theory is that Mithra originated in Persia, and Isis came from Egypt who were both trade partners with the expanding Roman Empire. Although Mithra and Isis were religions, they weren't exclusive, and you could worship both the traditional Roman pantheon of borrowed Greek gods albeit with different temperaments, or whatever religion your parents had before they migrated, sold into slavery, etc. to Rome.

So, if he worshiped Mithra, he might also have a personal deity, usually Apollo or Zeus, if your mystery Mithraic man lived in ancient Rome. If that's the case his wife might openly worship that character as well, while either staying home when he was hitting up the Mithraic bathhouse or meeting cave, or if she was particularly outgoing, she might have adopted worshiping Isis in her free time, which was also a very popular religion at the time and was open to women.

The cult was certainly for men only. As Gadern notes, Isiac worship (cult of Isis) is probably the closest equivalent we can cite to Roman Mithraism that accepted women. This was another eastern "mystery cult" which drew its appeal from the deliberately arcane and secretive nature of its activities. However, the similarities are quite superficial. The answer to this question is extremely broad- there was a whole host of deities that one could draw on that were not mutually exclusive, and these would vary depending on where and when you were in the Roman empire.

In fact, given the strong correspondence between Mithraism and the military (especially in the north-western provinces, where mithraea show a strong clustering along the limes), and the fact that the common soldier was (in theory if not in practice) forbidden from having a wife (although this later changed) when serving, this hypothetical situation may have indeed been less common than one can assume. Even in the case of married mithraic initiates, it is more than certain that they would have revealed hardly anything about the cult activities to their spouse- as far as we know, nothing regarding the cult practices was ever even written down by Mithraists themselves.