Can I encourage you to invest in some help? Even if it's a neighborhood girl willing to come in and help while your at home? I started doing that at age 11 and continued until I turned 18. Some moms were just overwhelmed. One had cancer. I made meals, did laundry, light cleaning, and took care of as many as 4 kids at a time. One mom just had me walk her newborn around while she took riding lessons. In whatever context you need help, ask for it. You might also be able to get some free grown up help by letting friends and family know you need it. If you have an extra room, you could offer to trade a college student help for free rent, even... Maybe you could offer to watch someone's bay overnight and they could take her for more active play dates. Unless it's inconvenient, consider sending her to daycare on days you have to take off for health reasons so you actually get the break you need. Etc.

You really have to nip that joke in the bud. Explain if you're unable to communicate to him how serious you find it, that perhaps it's time for you two to start couple's therapy. --And I'm not joking or kidding about that. He is slowly poisoning your relationship.

My son was a very similar baby to yours, he slept well and long, and rarely cried, unless I wasn't at home. My ex, only had to take care of him two nights a week while I was attending college. Although he spent a few hours, every day, at the gym, he complained constantly about having to carry him while I was gone to keep him from fussing. It annoyed my mom to the point that she just took over to shut him up. He could bench press more than his own weight, but couldn't lift a 10 lb baby? It was not a good sign of things to come.

In some they're harder to take care of as infants, and in some ways they're much easier. It's reasonable to expect you're going to need more supplemental care for your sake and hers at different stages of her development. I know you expect the world from yourself, but it's okay to admit you need help.