Hi...

My husband and I got married in June of 2009. He lives in NY & I live in CT. Our son lives with him & my father lives with me (yes he is a qualifying relative). He has a business in NY and no income in CT. I have no income other than CT unemployment. Can we both file as HOH?

No, none can be head of household.
You can file joint return or as married filing separately.
For head of household you must be unmarried or did not live with your spouse for last six months of the year and have a qualifying dependent and pay more than half the cost of the household. Your U.S. Tax Return: Filing Status: Head of Household

But we did not live together at all.?

Perhaps for tax purposes you can consider yourself to be unmarried. As long as (a) you didn't live with your husband for at last the last 6 months of 2009, and (b) you each paid for more than 1/2 the upkeep of your home, then you can be "considered unmaried," which woiuld allow you to both file as HoH. However - I have a question: have you run the numbers using Married Filing Jointly? I would bet that this would result in a lower overall tax bill for the federal return. And as for the state taxes - you can file as Married filing Separate in CT and your husbamd can do the same in NY, since you were each full-year residents of your respective states, and neither of you have income sourced from the other state. So in the end I don't see why you would want to file as HoH.