Should I walk away or stay and try one more time

Hi Everyone,

I married a 26 yr old man from Lebanon and I am 35 female. I did a lot and invested a lot to bring him here. When he came things were rocky with adjusting to cultural differences as well as personality differences. I had been concerned with some of his actions and kicked him out in July 2015 (only after him being here for 6 months). I took him back and from there things went down hill. He has a habit of living a secret life and will make multiple accounts on Facebook and IG. I found him talking to girls online and from that point I asked him no social media (he also didnt want me on there as well). We both agreed and promised. Fast forward through our relationship and we endure lots of fighting over trust issues and me asking him to leave then coming back. In October of this year I asked to look through his phone because he wanted to look at mine-fair is fair. I found a post he made advertising online looking for women. At this point I said it was over and he begged me to stay stating that he made that when things were bad and nothing ever happened with it-he only posted. I lost all trust but stayed because I truly love him and believe in staying in a marriage and not leaving. A week ago I broke down and looked at this phone again. I found in his internet browsing history he was on Facebook again and his history showed about 10 girl names he had clicked on (I couldn't log in so I don't know what this entailed). Also he had googled a picture of one of the girls he worked with and searched for her on Facebook as well. Before I told him what I found, I asked him if he was on any social media and he replied no. I said none at all? He said no. I showed him the screenshots of all the pictures I had taken on his phone and only then did he say ok I was. He constantly lies to me and then only admits the truth when cornered. I ask him how he can do this and he says he doesn't know why he does-he does it to avoid fighting.

He said he wants me to stay and we try couples therapy-but for me how will this change his behavior? He told me that the reason he keeps doing these things is for a distraction because things are bad with us and he feels like I judge him and am never happy with him. I told him if he was so unhappy he could end it or suggest counseling or talk to me--his method of dealing with it broke all his promises and led him to constantly lie to me and ruin any trust. Of course to add to all this his company is closing and he will need to relocate to another state and wants to me go. I cant do this and chance losing my job when we are bad. He was so upset over losing me he told me he would not take the job and try to find another one here. I feel that maybe because we are so unhealthy that he shouldn't lose a good job opportunity and this is the chance for us to end it. He is very upset and feels that I am running away and giving up. He said he loves me and accepts all my faults and why cant I love him and accept he has faults. I am very confused and feel that if trust is gone and someone keeps betraying you they will keep doing so. I just wanted to hear any other comments that someone can offer. I should mention that I was married before and that marriage was ruined by that husband cheating multiple times. I told my current husband what that had done to me and how damaging this was and he promised he would never hurt me in that way. I feel so betrayed and hurt.