Ah, but wouldn't he therefore have a baby? Perfect tense?
'Had' is past perfect tense, which is fine when used to imply giving birth to a child, since that happened in the past and is over.
But, if he still has the baby, then it wouldn't be past perfect (or I suppose it might be called pluperfect, don't really remember) tense, so you can't say "he had a baby" unless you're either referring to him giving birth to a baby (as if you could give birth to anything else), or if you're referring to him having a baby at one point in time but no longer having it, i.e. baby turns 18 and moves out, although I figure that as long as you still have contact with the child, you would still 'have' him or her.