It's an old, old story. The mom is seen by the dad as the primary caregiver for infants. Yes, there are exceptions. Yes, in an ideal world, all dads would share more of the work around the house and be more involved with their children.
Unfortunately, many "real" husbands' expectations are that they did their wives a favor by impregnating them, because it was the wife who really wanted the child(ren). Many men behave as if they did their wives a favor by simply marrying them and giving them a home to run, too, so why should wives complain?
So that's one component of "the way things are," and if wives stay focused on those inequities, nearly all marriages will eventually fail. You don't say how long you've been married, whether you mutually wanted this child, how much you talked through beforehand about who agreed to do what.
You do mention how hard your husband's work life is, and he may see your staying home as a great blessing he's making possible for you. And perhaps it is. If that is just as true as you not having the freedom to "get up and leave town," and that you "would not even if I could," then you might be able to balance your resentment with an appreciation of what he is providing for you, for the sake of making your own thoughts easier to live with.
Resentment (even if you deserve to indulge yourself) will eventually poison your marriage. Not wanting others to have something we are denied, especially someone we have promised to love and cherish forever, is a rather unforgiving place from which to nurture a long-term relationship.
I'm guessing that if you can throw yourself heart and soul into mothering and "wifing," ride out these demanding early months of your child's life, and stay positive and loving, your husband will begin to interact with this baby as it grows older and more responsive. Continue to ask for what you want clearly, because guys are generally incapable of taking hints. Perhaps you have told him clearly that you want him to stay home and participate more, that would be one thing. But if you haven't, don't expect him to "get" why you are resentful.
And consider cutting him a little slack after a day at work. Falling asleep feeding the baby may be nothing more than he is too tired to stay awake.
If you can't "educate" your husband in the nurturance and companionship you'd like for yourself and your child, consider counseling. It can be tremendously helpful in sorting these issues out.