Hi Gail,
It would be best to draft a financial settlement agreement with your ex husband since you two have separated. You do not have to cover all of your assets as yet, but it is best to get something in writing so that you have support for what you are claiming.
Your ex husband bears the full legal responsibility to pay the utility bills. However, he may seek indemnity from you as you were the one using living in the house and using the utilities. This is unless you have something in writing or recording or by some other means that can support your claim that you need not repay your ex husband. In other words, while you may have a legal right not to pay, if you don't have any support/evidence to point to this claim, it is very difficult to fight your husband about it. However, I would negotiate with your ex husband, explain your situation and hopefully can come to some arrangement. Once you do, record this arrangement down in writing. or make a personal note of it in your file.
Aside from this, as Sophea has recommended, take a financial inventory of your joint assets, your personal assets and your ex husband's personal assets (i.e. those owned in his name). Have a look at this thread for separation asset/financial division advice. There are many threads under "Family Law" that talk about asset division in divorce and separation situations.