I agree. If all the husband is doing is chatting online to ex girlfriends, that wouldn't be seen as a reason to leave the marriage over here, although I realise that it's upsetting that he won't stop when he knows you don't like it. If you can try not to show you're upset and even pretend you don't mind, he might even stop doing it or let you look at the messages.
Try to talk to your husband along the lines of "I'm finding this difficult, but I am trying to understand your culture" rather than accusing him of lying.
We behave in very different ways here from what you're used to. I have male friends who come and stay with me in my house for several days at a time, but there is nothing sexual between us. I wouldn't want to be told not have them here anymore, as I'm doing nothing wrong.
Don't read too much into your husband keeping his debt secret. He probably didn't want to worry you, or was concerned the authorities would find out.
Try to find some other Filipino wives to talk to and ask them to explain the English male to you. Oh, and if you find out, let me know! We English ladies are still trying to work him out.