brown I've not had that specific test but absolutely yes it is possible to have both alloimmune and autoimmune problems - I have both. And yes you could have one child with your DH and still have DQa problems. My OH and I are 100% matched for DQa (we are both 0201,0303) and this means that any embryo has a 50% chance of being a direct match with me, meaning my body would kill it off as not being 'different' enough to me. But equally that means any embryo has a 50% chance of NOT being a match, and so (theoretically) would be ok.
To explain a little, if this doesn't make sense, since an embryo takes one marker from each parent, it could end up being one of the four following possibles:
0201,0201 (one from me, one from OH)
0303,0303 (ditto)
0201,0303 (exact match for me)
0303,0201 (ditto)
So in the first two cases the embryo would survive, since it is sufficiently different to me, but in the last two cases it would be destroyed.
Hope that helps, a little!