1 Cor 7:12-16: "But to the others I say, yes, I, not the Lord: If any brother has an unbelieving wife, and yet she is agreeable to dwelling with him, let him not leave her; 13 and a woman who has an unbelieving husband, and yet he is agreeable to dwelling with her, let her not leave her husband. 14 For the unbelieving husband is sanctified in relation to [his] wife, and the unbelieving wife is sanctified in relation to the brother; otherwise, YOUR children would really be unclean, but now they are holy. 15 But if the unbelieving one proceeds to depart, let him depart; a brother or a sister is not in servitude under such circumstances, but God has called YOU to peace. 16 For, wife, how do you know but that you will save [your] husband? Or, husband, how do you know but that you will save [your] wife?"
If you are agreeable to staying with him, per these verses, he should let you, and he should stay with you. If there are other problems, that's beyond the scope of these verses.
Best wishes, however it turns out.
EDIT: I spoke before reading the whole thread. If he's cheating, the above verses don't apply. If you think it's worth trying to save the marriage, by all means, do. If not, move on. I don't want to sound callous, so if I do, I apologize in advance. I totally understand a bad marriage and what it can do. I'm living in one. Again, best wishes to you, however it turns out.