This is not healthy and if not stopped, will cause ruin in your marriage.
Men do not just have woman friends they call and speak to at lengths daily and want to take on vacation, there is something more intimate going on here. No, nothing physical may not have happened yet, but just his feelings for her are intimate, too personal.
I went through something similar with my husband 10 years ago. Same thing actually, I looked through his cell bills and I called her and she assured me everything was fine and they were just friends.
It wasnt but a few days later when one of my husband's friend's wives came knocking on my door to tell me that she had decided she had to tell me about this other woman. She said she had been thinking about it over and over and if her husband was doing this she would want to know. She told me about how there was a joke that his friends called her his "counselor" and she told me she was a married mother of three who lived NEXT door to my husband's mother and father.
Do not allow this to continue. Your husband may be bitter, you may lose him, but you are losing him anyway if it continues. Stand up and try to save your relationship from this, I did and I won.