Okay first off, because it is often blatantly misunderstood, I believe that opposite sex and same-sex friendships with someone who is gay, are life enhancing and I wouldn't be without them.
However, all such friendships should have some boundaries, because it would be wholly disingenuous to pretend that it is possible for those friendships to cross the line, especially when that friendship is new.
These are the factors that make such a friendship unsafe. If there is:
- Secrecy, either about the existence of the friendship or the interactions within it.
- Physical chemistry.
- A situation when the friend knows more about the person's marriage, than the spouse knows about the friendship. Typical of this are when intimacies that are normally reserved for a romantic partner are being shared with the friend, or when the attached person is complaining about their dissatisfactions with their marriage, either real or manufactured for the purposes of this friendship.
From what you've said, these are secret friendships and we don't know the rest. There's no earthly reason for keeping a friendship secret from a spouse, unless that spouse is irrationally jealous and would try to forbid any friendships with the opposite sex.
However, if this is the case, there are more pressing problems than infidelity and it is far healthier for the non-jealous spouse to confront the issue, reassure and demonstrate transparency and openness, encourage one's spouse to meet the friend and maintain the right to have safe friendships.
Another general rule of thumb in these situations is to ask oneself "Does this friend wish my marriage harm?" This is what's meant by the term "friend of the marriage", a ubiquitous term for someone who is benign and wishes no harm.
What often happens is that these friendships start and there is a process of mirroring eachother's interests and values. However, since this also tends to happen in safe friendships, no great danger is perceived, but if physical attraction is also present and the spouse at home is being disparaged by either friend, the warning claxons should be going off.
If you are already invading your partner's privacy and finding evidence of secrets, only you can tell us why you think he is keeping these secrets. If you're someone who is perfectly relaxed about safe friendships with women, but think your partner is an opportunist and flirt, there's more reason to worry. If on the other hand, you know yourself to be irrationally jealous and insecure, confront that issue first, because sometimes it leads to the thing you fear most, anyway.