I don't think that Barnabas would have ever considered biting Joshua and turning him into a vampire, much less anyone else in his family. The nature of his curse and Angel's curse are completely and utterly different. As someone already pointed out, vamps on B&A go soulless, as demons who are just evil things who do bad stuff because they want to have some giggles. Barnabas, on the other hand, while being "evil", was not evil per se. He had his moments, of course, but if we compare him to Angel, I think its fairly safe to say that Barnabas was in possession of his "soul" or "conscience" during his vampirism. Angel did very naughty things while having his soul, and Barnabas did equally, if not worse, things while supposedly being on the side of "good".
One of the things that makes the vampire lore so interesting are the varying degrees of interpretation that can be attached to it. I don't watch Moonlight, but from what I've been reading about it, while it shares similar things to previous vampire shows, like Angel, it is, in fact, quite different, and has a different set of rules by which Mick St. John can exist. If I recall, before the show went into reruns because of the strike, Mick was human because of some potion or spell, at least that's what I read. That happened in DS, when Lang cured Barnabas, but never happened in Angel or Buffy as far as I can remember.