1. would the child be a dependent for both of us-- Me filing HOH and he filing single?
Yes - the child will be a qualified child for both parents as they are living together - but you may not both claim the same dependent - you need to decide between yourselves who will claim the child.
But only the parent with higher AGI is generally a head or household.
2. do you use the special rule or the tie-breaker to determine dependency?
Yes - there are Tiebreaker rules. There rules are used if both persons are eligible to claim a child, but could not agree. To determine which person can treat the child as a qualifying child to claim these six tax benefits, the following tiebreaker rules apply.
If only one of the persons is the child's parent, the child is treated as the qualifying child of the parent.
If the parents do not file a joint return together but both parents claim the child as a qualifying child, the IRS will treat the child as the qualifying child of the parent with whom the child lived for the longer period of time during the year. If the child lived with each parent for the same amount of time, the IRS will treat the child as the qualifying child of the parent who had the higher adjusted gross income (AGI) for the year.
If no parent can claim the child as a qualifying child, the child is treated as the qualifying child of the person who had the highest AGI for the year.
If a parent can claim the child as a qualifying child but no parent does so claim the child, the child is treated as the qualifying child of the person who had the highest AGI for the year, but only if that person's AGI is higher than the highest AGI of any of the child's parents who can claim the child. If the child's parents file a joint return with each other, this rule can be applied by dividing the parents' combined AGI equally between the parents.
See IRS publication 501 page 15 for examples of using tiebreaker rules - http://www.irs.gov/pub/irs-pdf/p501.pdf
Let me know if you need any help.