Oh boy, where do I start? I want to approach both Sers' and Augustana's situations at the same time, although that might not be best to do it only that way.
First off, I have to be self-centered and say something about myself, if only to try to clarify why I feel I may not have as hard a time with certain situations as some other Asperger's people do. I seem to think at a high "rate." I think that's my main help, in that I intellectualize things so quickly that I can get over a lot of situations within a few seconds to a few minutes to a few hours of thinking and talking something out. It's not that I don't have difficulty. But I seem to be able to talk myself into and back out of situations in my head more quickly than most, if not all, people I know...in a rational sense, I mean. If I could imagine NOT being able to do that, I can see myself having all sorts of strong aversions to things like small children and their ickiness. I mean, I do have those aversions, but they generally do not overwhelm me.
Yes, children are gross. I mean, I can relate to that aversion to small children, especially when they get poopy, sticky, food-covered, etc. I can usually "get over" most of it because I tell myself a lot of (complex?) intellectual things about how there's no way out of the reality of life and it's dirtiness. If I were not able to tell myself such things and to get myself to (mostly) believe them, then I could see myself obsessing over touching toilets and door handles and trash and, well, let's not get started with that list. I'd be something of a hypochondriac or develop OCD toward cleanliness. However, I mainly tell myself that my ancestors have been dealing with filth for a very long time and it didn't necessarily kill them (at least not by itself). And I see that if I wash up everything systematically and thoroughly after a mess, then I generally am going to survive the experience and not kill myself.

But, keep in mind that even if I "get over" things for the most part, what does NOT change is the need to be careful and systematic when I do things such as cleaning up (yes, even cleaning my children).
So, basically, I have to analyze my way out of worrying too much or feeling too grossed out. I'm not saying that's going to work exactly the same for everyone. But, it can help to be aware that it helps, if that makes sense - basically, education and analysis are the main ways "out" of "sticky" mental situations which cause anxiety and obsession. I can't be so presumptuous as to say that it's going to work the same for everyone else as it does for me. But that's the main way that I get out of the sticky situations in my head - analyze...and if I don't have any "answers" yet, try to be patient and wait and don't make too many assumptions based on my reactions instead of based on what I actually have reason to believe.
I'm not sure how I would translate these ideas to your husbands [talking to anyone here in a similar situation as Sers and Augustana]. But that's partly because I don't know them, of course. However, I think if I were to talk to them, I would have to bring up that idea of analysis sooner or later. It's unavoidable, eventually. It's the only thing I know "works" from inside my own mind. We have to question our assumptions - I think that's true for anyone, but in this sort of situation it applies to us who appear to have Asperger's.
And yes, Sers, it can get easier to relate to your children as time goes. But perhaps it may be useful to note that, out of necessity, I have to look at my kids as a responsibility first. I'm not sure, because I'm pretty sure I'm not normal

- but I don't think that's how my wife, for example, looks at our children. She probably, as a woman and as a more normal person, usually has feelings of love and attachment first and then thinks about the responsibility after that. I'll venture out and say that it is probably typical for an AS person to do it in the reverse order. I'm pretty sure of that because I see that "we" do most/all things in a reverse order in terms of things that we usually call logical versus emotional. I think most people start with emotions and then possibly, if they have the time and determination, break through those emotions to think about things more logically. People with Asperger's, I would argue, tend to do the reverse.
Sers,
I personally try to relate to children a little more readily than your husband seems to at this point in time. But, I mean, I have long been determined to be a father someday and to try to be damn good at it (meaning my best, at least). I have a heart for it. I've thought a lot about it. And so, I might have a little bit of an advantage just in terms of my sheer determination. I actually have spent considerable time obsessing over and criticizing some of the lax parenting that I do not agree with and the way that fathers are sometimes disengaged (not just AS fathers), among other issues. So, that's been important to me. I don't know everything ABOUT parenting. But I sure as heck never questioned for a second that I CARED about it. So, I feel strongly about that.
Even if your husband is not exactly like that, it doesn't sound like he's the exact opposite, either. I can't seem to avoid saying this next part. So, here goes: He's going to have to learn to do some things just because it seems to help the child, not because he necessarily understands it. I'm not saying that he shouldn't understand it. But I am saying that the AS tendency to need to rely on logic or analysis makes it difficult for AS people to act quickly or to "accept" things. I hope you can at least get your husband to talk about this (though not necessarily all at once), even if you don't use the term "Asperger's" (because the term is kinda beside the point anyway). If you can at least get him to talk a little, you can talk to him about the idea of just trying to trust that at least some of the things that you do or that others suggest to take care of his child are profitable. With that said, if there are particular things that he is extremely uncomfortable doing, it's probably because he does not "understand" the need for those things. And you may want to try to do those things that he is not comfortable with, so that he has time to think it all over for himself rather than feeling forced to do something that he feels is somehow illogical or unnatural.
Stop me if you think anything I'm saying is to "out there" and too much of a stretch for you to understand.
But, I actually need to get off here and go make lunch for my kids (speaking of kids).

cheers,
Dave