If you are married, can either file their taxes as Head of Household?

Also, which is better to file...Jointly or Separately? My husband did not file for 2006 because the return said he'd get $ back but then it was rejected and said he owed about $1000...I would guess separately. Also I am the only one that can claim my daughter as he is not the real father and has no legal right to her...right?! Thanks in advance!