My husband texting another women

I had a feeling something was up with my husband lately but today I woke up at 5 am to see him outside smoking a cigarette on his phone. I told him it’s late and to come inside to sleep. And he listened and went in but I saw his phone and put his flash on cause I was turning off the lights. When I got this feeling to look through his phone. Literally all I did was type his password and there it is. A random women in my husband phone that she replied to my husband when he wrote “I’ll be waiting” and her writing “keep waiting” and a meme of two random cultures marking out with each other. So I asked my husband you know what the fuck lol. And he kept trying to take the phone from me the women also has a boyfriend. But like why are y’all texting at 5 am and had deleted messages? So I told him and my husband doesn’t like to lie but would try to avoid the question and he said that he met her boyfriend before and that she isn’t his type. And they were on an online Russian class. But my husband keeps saying that I’m at fault for going through his phone and I’m the one that’s crazy. Am I acting crazy or do I have the right to see his phone and accuse him?