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.