There's a difference between what your husband is doing versus what the OP is doing.
You weren't having an affair. Your husband took something out of context and even when you explained, he didn't believe you, which is why he's still bringing it up now.
That's not the same as when someone just knows it instinctively that something is going on and so faced with an uncommunicative/tendency towards lying partner they go through the phone. Whether they find evidence then and there or whether they find out at a later date that there's an affair, the issue is that there always is something and their instincts weren't wrong.
Nobody advocates going through a partner's phone on a regular basis to check up on them "just in case". That's controlling behaviour.
You should be able to change your password without fear of reprisals. You shouldn't be treading on eggshells, knowing your partner will go through your phone and worrying about them taking something out of context again. That's not normal or ok.
Change your password. If your partner blows up about not being able to access your phone, LTB. If he uses verbal or emotional abuse to force you to give him your new password, LTB. If he brings up the thing from before again, tell him he either trusts you or he doesn't, so either you move forward and he never mentions it again or you split up. Trust, once broken, has to be re-earned, but you didn't do anything so that doesn't apply here. So either he lets it go, whatever it was he saw, or you split up. Because what's happening currently with your situation is an unhealthy relationship and he's being controlling. You shouldn't stay with these dynamics, it's not good for you.