My (42f) husband (44m) cheated last year, we reconciled but now this year I finally read messages.

I don't want to make this long so I'll be quick. Married 7 years. Last year we had a LOT of problems and at one point even talked about "taking a break". Honestly most of the problems (from my perspective) were due to his issues (he had stopped drinking, he was between jobs, his mother was ill). He wasn't treating me well at all and it was a very difficult time.
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I found out he was texting an ex colleague of his (a woman). I felt very uneasy about this and he was quick to reassure me. This was an "issue" for about a month because he would tell me he'd stop texting her but then I would see again that he was texting her, and he would reassure me there was nothing to it, etc. I asked to see their correspondence but he deleted everything, causing me to be very upset and uneasy, which is why I started talking about taking a break in the first place.
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Basically the whole time he was reassuring me, he was ****ing her. In the end, he left her and stayed with me. I found out when I borrowed his phone and she texted him a long, angry rant.
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I left for a while but we decided to go for therapy and work it out. So this was last year. This week, my phone died so I charged up my old phone. I know I shouldn't have done it but I couldn't stop myself. I re-read our texts from that time period. And I saw, with fresh eyes, each time he lied to me. Over and over and over. Lied about not talking to her. Lied about not having seen her in a year. Lied about not finding her attractive. Lied about his whereabouts several times.
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Even though I already knew this stuff, seeing it in black and white on my phone just was a punch in the gut. It was last year but it doesn't feel that long ago. I remember each of those days perfectly. I remember my stress and insecurity and how much better I'd feel each time he'd reassure me. Little did I know he was telling lie after lie.
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Now I want to scream at him. Is this normal? Is this part of the healing process? Or is it a slap upside the head for me to realize that he was a complete liar and betrayed me and I should leave?
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tldr: husband cheated, we stayed together and got therapy. Now one year later I re-read OUR text messages during that time period and I can't believe what a liar he was.


Source.