should I believe him...

so my husband was sneaking behind my back and talking/texting another girl for a month or so, we were in a rut I can honestly say, in March he told me he had cheated on me with said girl, he went out to the bar that night it was st pattys, I was suppose to meet up with him and he ignored me for four hours then said to meet him at home, when we got there that's when he told me he had. I guess he was complaining about me at work saying I was boring, and that he didn't want to be with me, and the only way out was to say he cheated.. with all that said we have never had a issue before he started this new job with this female... he flipped out and left.. and the next day he was texting me and saying he can't live without me, it never happened, he just talked to her cuz she was nice. he swears up and down nothing happened is willing to have pp vouch that nothing happened and even take a lie detector, I don't know if I should believe him or not or if this is a empty promise because he knows that ppl will stand up for him and we will never be able to afford a test... also he s on my phone plan I blocked her number and he deleted all of social media ...