Sory - didn't mean to imply you anything derogatory about your behaviour, just sometimes I worry that women especially can over-obsess about partner's behaviour to the extent that it can drive them further away.
If you feel are feeling seriously upset about this whole thing surely the best approach would be a frank discussion with your partner so he can understand that the way he is behaving is upsetting you.
The choice is then his - you have made him realise that if he takes this further, he will be eroding the relationship even more to the extent that it may become irreparable.
Communication has to be better than snooping and sneaking, surely? I just know that I would never, ever take a step like hiring a detective. I would find it degrading for everyone involved including myself and I would resent paying money to someone who makes a living in such a manner.
If I strongly suspected a long term affair which I was not prepared to put up with, then I would confront him personally. His behaviour at this point would tell me a lot about whether I wanted to make a go of the relationship. If he continued to lie or, worse, make out that I was crazy, that would be a deal-breaker for me as it would add insult to injury. If he was suitably contrite then I might be prepared to give the benefit of the doubt and make a go of the relationship.
How he responds to your upset is surely the key here?