Does betrayed spouse have the right to read cheaters journal?

I found out in Sept of 2013 that my husband has been unfaithful. I thought I could forgive him and we could work things out in our marriage. Since Sept I’ve found a lot of information. My husband only shared bits and pierce of his affairs with me. Lying about how many women he sleep with, how many times it happened. How many women he talked to online and on the phone. I’ve would ask him the same question over and over “have you told me everything” and he would give me the same answer “yes” only for me to find out one more lie, one more girl. I’m love my husband and want our marriage to work. I feel that I’m giving 110% to recovery and trying to find out what happen and to fix the problem. The biggest issue I have is I don’t trust him.

We both go to therapy. If he ask me what I talk about during my session I tell him. I tell him everything, even if it is hard for him to hear. I believe in being honest and not having secrets. Clearly my husband doesn’t feel the same way. He won’t share anything he talks about in his session.

He started writing his feelings in an online journal. He sent me a few of his entries where he stated that he hasn’t been “in love” with me for 4 years now. (around the time of the first slip) . He also shared that he is hiding a part of himself from me and has never let me in 100%

Do I have a right read his journal? He tells me that it’s his personal, private thoughts and I don’t have a right to read them.
But I think if he wants our marriage to work he needs to be 100% open and honest with me.