My Xh never put kisses on texts to anyone but me, until he got friendly with OW. She puts xx on messages to all her friends... he then put them on all messages to her. They claimed that they were supporting each other.
He was texting 100 times a day, as soon as he left the house, right through the day, and after I had gone to bed. Emailing her, ringing her, all to give her "emotional support" and ALL of it was hidden from me. his phone was chained to his side, he slept with it and I was no longer allowed to touch it. I never gave it a thought at the time, as I trusted him.....
When I confronted him , having found mobile records and emails, (he had already left by then, having suddenly walked out claiming that he no longer loved me), he said that he didnt contact her that much, that they were just friends, that her H knew (his best mate......).
I divorced him last November after he left at Easter. He is still contacting her behind her H's back.
What your H is doing is not right, anything that is hidden from your partner is wrong. if it was genuine and he had no feelings, he would say oh X is having a bad time, I have been texting her to make sure that is OK, I hope you dont mind.....
Your H is bang out of order. I am really really sorry that you have to go through this, but you need to get tough with him, tell him that you do not accept that he is in contact with another woman, that he has to cut all contact, or he can sod off.