Hi yorkiegirl, so sorry to hear this girl is still in your lives. This sounds so familiar (as you may recall) my dh did have an affair last year, started very innocently - a friendship with so at work, email, texts then meeting for coffee, lunch then finally onto a full blown affair. My dh somehow managed to find the time to meet her whem I thought I knew where he was. i never questioned as I'd never had any reason in 16 years of marriage to doubt or distrust him. Even when it came out that he had been having an affair it took him far to long to completely stop contact with her. When he finally "came to his senses" ( his words) mid life crisis type thing!!!)she wouldn't take no for an answer and we had several months of her trying to contact him any way she could- emails at his new work, ringing him at work, letters at work,etc etc It wasn't until this point that my dh finally started working with me not against me that I knew he'd got her out of his system and we faced the problem together. I met her, her dh, her parents during the course of the year when this was going on. There is a huge sense of fantasy about a relationship over the pnone/ texting that fantasy becomes much harder to sustain when the elements of it you don't want to think about(ie his wife and kids) start to get involved in your life. It took that ( and nearly tearing our marriage apart) before both dh and then eventually her realised they could not have any contact whatsoever.
It may be your dh has not got as far down the road as an affair but by the sound of it he's heading that way ( my dh who can talk about it now, after lots of counselling for us, says each little step into the affair was just a little step until before he knew it the next little step was sex etc!!)You must tell your dh how you feel and make him see how this appears. If the tables were turned would he be happy you having this relationship with a man? Until he starts working with you on this there will always be that element of mistrust which is so destructive to a relationship and eats away at you, believe me. If he's lying to you then he's something to hide and has given up the right to privacy ie his phone- check it, question him make him feel uncomfortable about this relationship with this woman it is not appropriate, especilly if it is threatening your marriage. remind him what he has to lose and for what ( a cheap thrill/ a boost to his ego.... my dh learne dthe hard way)please talk to him, it won't go away by itself!