I think it depends on the amount of time spent with the third party in question, especially if either spouse is absent. If I was married, I don't think I'd have any issues with my bride having a male friend...but if she started spending large, consecutive amounts of time with him, and I wasn't around, I'd get very worried. Trust in any relationship has to go both ways, or else it doesn't work.
Just as an example, I spent a lot of time with my female friend back when I still lived in California.
Her boyfriend / fiance / husband worked construction, and was gone for long hours during the day. He'd even be gone for days at a time, even a full week, being out of town for work. I'd spend lots of time with her during these periods, and this kind of stuff went on for about 2 years or so. Her and I would go out for lunch or dinner, I would give her rides to her work, or to doctor's appointments, or go shopping with her, she'd call me up at night to hang out because she was "lonely" and wanted company.
None of this activity ever turned sexual. Never in the least bit. She was an attractive girl, I'll admit that much, but the relationship her and I had was more along the lines of a brother / sister relationship than anything else. There was no sexual or romantic chemistry between us in the least bit.
Her and I spent so much time together that she eventually asked me to move in, and I lived with them for a short time.
Where the trust was came in the fact that we never hid anything we did from him. If I was over at the apartment with her, she always told him. If her and I went out to lunch, he knew.
Her and I were upfront with each other that our feelings only extended as far as a strong friendship. Her and I always had communication with him over what we were doing. All 3 of us trusted each other to not do anything to disrespect the friendships or the relationships.
Now I can understand that it would be hard to have that kind of trust. But having been the "friend" to the girl in this type of situation, and knowing that I never once felt any desire to betray her relationship, I know that males and females actually CAN be friends. I've been friends with the girl that I spoke of in this thread, I have spent a lot of time with my best friend's girlfriend, even so much as taking her out dancing, as well as another very good friend's girlfriend, all without anything ever happening, or even anyone WANTING anything to happen.
I will admit this much - if I were the guy in the relationship, and my girlfriend were constantly hanging out with a male friend, it'd be hard for me to not think the worst. Especially considering that I (unfortunately) have a habit of over analyzing things to begin with.
But if you are truly in a healthy relationship, then you should be able to trust your significant other to make the right decisions around the opposite sex.