It must have been infuriating hearing that patronising remark from him, especially as you had made things easier for him in advance, but maybe he feels his parenting is being judged and this was a knee jerk self-defence response?
It appears as though he doesn't respect the amount of effort you put into their care, and thinks you are making a fuss about nothing, but maybe he is embarrassed about not having a clue what to do and thinks its best left up to you? I often heard comments like this from my husband when my daughter was very young (5 and under) which made me feel totally undermined, and made me wonder sometimes if I would have coped better without him judging/criticising my parenting style. We got through it eventually, and she's grown into a mature, wonderful 21 year old, however I still think he fusses over her too much (constantly offering lifts etc) but I joke with both him and her about how much he dotes on her - but I don't feel in competition with him, as I know she respects and loves me just as much, as I can help her with things that he can't and vice versa.
It does sound as if you need some practical hands-on help at this stage, maybe one evening you should arrange a babysitter (if poss) for both you and DH to go out for an evening to talk about all the practical ways he could help you (without getting irate/critical or overbearing with him) and talk about what's putting him off from taking a more active role - it could simply be he feels inadequate dealing with them and doesn't want to be embarrassed in public with them, hence seen as a 'failure' by other people, on the other hand he might claim to be too tired - well that's no excuse and he needs to consider how tired you are as a consequence of doing it all on your own.
He really is the only person, from what you said, that can make this situation more bearable for you (and enjoyable for your boys) and, as their Dad, stepping up to his role will really increase the bond he has with them - best time to work on it is now, while they are young, as it will become too awkward when they are older - if your relationship can last, given the lack of his input!