Well, I think a big point is to acknowledge your DH's wonderful protectiveness of you. Sometimes husbands and wives go head to head about this when really they want the same thing - what's best for the family. Obviously the specifics of what's best are often in disagreement, but if you start by positioning yourself and DH on the same team, it helps.
Next, you'll want to respond to his specific fears. Obviously the cord around the neck is a big one, and it was for my DH too (his sister had that). We were all (including me) surprised to learn that this is common, not a big deal in the slightest, and handled by a midwife the same as a doctor handles it (except the doctor makes a big deal out of it, and the midwife doesn't

).
I don't know what happened with your 3rd stage labor, but it is likely they overreacted and possibly put you in danger with their intervention (it is VERY risky to pull out, even if gently, a placenta - risk of bleeding out). A midwife is used to this kind of event (not even sure if I would call it a complication).
Now, the next trick is to get your DH to name all of his other fears so you can both research it (or probably it will be just you researching but reporting to him). What I personally have found - and you'll have to find for yourself too, to make this decision - is that there are very, very few true emergencies in birth. By true emergencies, I mean events that require immediate intervention to prevent serious injury or death. One of those emergencies is prolapsed cord. But the chances of prolapsed cord go down with a homebirth because a midwife is much less likely to do routine rupture of membranes (which increases the chances of prolapsed cord).
With my DH, the more he heard of this stuff, the more he was convinced that hospitals are dangerous places.
To be honest, he never got over his anxiety 100% but very few men do (I don't say that none of them do, I know another man who actually was the one who convinced his wife to do a homebirth). He did however decide to support me on this after we addressed his SPECIFIC concerns (you can't address a vague concern like "something could happen" - well, what?) and he saw the pattern of intervention that often causes problems, and then the hospitals take credit for "saving" the baby (or mama).
Oh, and men like numbers and studies. This recent one showed similar neonatal deaths for low risk home births and low risk hospital births (translation: home birth is JUST AS SAFE as hospital births for low risk women) plus reduced interventions (so not only are the statistical outcome of death the same, but the general problems are REDUCED for home births):
http://bmj.bmjjournals.com/cgi/conte...505/1416?ehom_