I think he’s cheating

I really feel like my husband is cheating. I don’t think he has had sex with anyone but I do feel he is communicating with someone via messages. I’ve noticed he has put his phone on airplane mode several times and puts his phone under the pillow at night. To some it may seem like no big deal, but it’s new behavior and I’m very suspicious. I of course have asked and he always seems to have a “plausible” reason. If he is cheating I will leave and won’t turn back, but I’m so uneasy I need to know. Is there any possible way I can read his iMessages from my laptop or my phone?? I’m desperate and talking to him won’t help because he will deny, deny, deny.

Update: I can’t call his phone company because we have separate accounts and separate companies. We both kept the same companies and numbers from when we were dating. I do know his Apple ID username and password. Thank you all for your comments. I do have the password to his phone and I have checked it and it has nothing. However, I know it’s possible he erased everything before he gets home because he knows that I have his pass code. I have asked him about his behavior and he says he placed his phone on airplane mode to save battery but why not just charge it? He had never done that before until a few days ago. I have decided to check his messages on my iPad by using his Apple ID. I hate to stoop to that level but I just feel in my heart something is not right and i won’t be that woman who turns a blind eye because she’s afraid to know. I think if do this on the iPad while he is sleeping I can accept the notification on his phone?