What's a girl to do when she finds her guy has been viewing on-line ? Isn't he supposed to know better?

He's "old enough to have gotten this out of his system" if it is just curiousity. This isn't the first time either. I consider it cheating, just like chatting it up online. It is kinda like...just one little puff, it always leads to something else. I am not a prude, I just think it is horribly demeaning to me and to women in general. It is all about trust and I don't think I can have a relationship with a man who views online while I am sleeping in just the other room. I snooped at the history when I woke up at 1 am and found him still online after I had gone to bed at 11 and had turned him down for "you know" for like the first time in like forever. I have teenage daughters in the house and I think it is just flat out wrong. He has asked me to marry him and I don't feel I can trust him. He always challenges me with...what about that unconditional love? I just know if the shoe was on the other foot that none of this would fly with him, how about you?