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you can't file a joint return if you are not married.

 

at best one of you can claim head of household by including the child as a dependent on your return. The other files as single,

 

who should claim the child? you need to do a series of returns one where he claims the dependent and head of household. you file as single. 

1) if both returns show refunds or balance due add them if one shows a balance due and the other a refund net the two

do the same where you claim the child and head of house and he files as single.

repeat 1 bove

 

the filing option that produces the smallest balance due or the largest refund should be best.