My husband and I lived in different states more than 6 months last year. My husband supported more than half of home expense and lived with our child. Can he fill as a head of household whild I fill as a married joinitly or a single?

No - he can't file as HoH if he is married. Why not file as Married Filing Jointly? This is probably best for you. There is no requirement that you live together in order to file as MFJ.