You can easily keep the house Elli, being a guy, its takes some pretty serious shit to make you make an about face like this all of a sudden. Not to be a negative nancy, but my moneys on the fact that he either is, or was, cheating on you and either a) feels bad and wants to give you your freedom, or b) wants to take things further with the other person.
Just my 2 cents is all.
P.S. Space is needed to heal w/e wounds will be left from this divorce, staying together because of "friendship" and "economical stability" will only aggravate those wounds even though its not apparent right now. Of course this is all advice and as we all know, advice is meant to be given, but doesnt HAVE to be taken. Good luck.