My H was worried that if I had any contact with OW, OW would lie and hurt the rebuilding of our M. I explained to my H that trust was a two way street and he had to trust that I would be able to see the truth from the lies....and that hiding stuff would only breed suspicion. He then made everything 100% open and I was involved in contact with OW and OW also knew that I saw all previous correspondence etc when she tried to get my H to leave me and be with her. She soon cleared off.
I know, in the beginning, even though my H was breaking off with OW, he didn't want her to be more upset than was necessary....he seemed to think more anbout her feelings than mine....but that soon changed.
Give it a while and see if your H relaxes about it all. If he doesn't I would then want to know why.
You could try reading some books about healing from infidelity with him so that he can see what it is recommended happen in order to rebuild trust - my H found that very useful....but then my H was really committed to repairing our M and he wasn't all defensive about things.
Saffie me 46 H 46 M in 1986 D20,D18,S16,D13 H's A 01/05 to 07/06 H recommitted to M 07/06 renewed vows 09/06 Going from strength to strength