There are cases in which I wouldn't mind one bit if my husband called up and said 'hey, it's late, don't want to drive, I'm crashing on XX's couch.' Ditto where he wouldn't mind one bit if I called up and said, 'hey, it's late, don't want to drive, I'm crashing on XY's couch.'
I trust my husband implicitly and the reverse is also true, but there are friends we have where this wouldn't be acceptable. It has nothing to do with my trust level in my husband, and everything to do with my trust level in a particular female - namely, I think she's take it the wrong way, so it's unacceptable.
If he called me up and said, 'I'm hot, Jean and I are going skinny dipping', I wouldn't have an issue either because I trust them both completely. However, if he called me up and said, 'Val said it's late and I should just crash on the couch', my response would be 'what the hell are you doing at her place without a chaperone, I'm dispatching the FBI hostage negotiation squad!?!!' because I don't trust her one bit and know she would try to create a compromising situation for him.
So, ask yourself, do you trust this particular female friend and are you comfortable with her spending the night with your man? If so, and you trust him, then it isn't an issue.
If you don't trust her, then it is an issue, whether you trust him or not (at the least, it's a headache you and he both don't need).
And of course, if you don't trust him, it's an issue, but a larger issue than just this particular event.
Frankly, if you can't trust your significant other to be alone with a member of the opposite gender, you should be rethinking the relationship or addressing your own underlying issues. Trust is vital to a working relationship.