It is important that you both come to an agreement of what "needs" to be done on a regular basis, and what is a job that can be done at greater intervals.
People's expectations can be VERY different of e.g. how often the floors need to be mopped and the carpets vacuumed.
Sit down together, and together come up with a list of things that needs to be done daily, weekly, monthly.
Be prepared to let some things go and to not have them happen as frequently as maybe you would like to have them done.
After you have agreed on what items need to be done (and do include feeding the baby, changing diapers, etc, but also mowing the lawn) and how often, then assign names to them.
Somethings may always be "yours" and "his", others you may take turns on a weekly or monthly basis, some things you may decide to do together and pull a joint effort at the same time, as a team, for example the weekly deep cleaning of the bathrooms, or vacuuming/mopping/dusting of the house. Or folding and putting away the laundry - that can easily be done together while chatting and catching up with each other, listening to music or talk radio or even watching TV...
Picking up the baby to change a diaper can be more easily done on a pitching in basis, whoever has their hands free at the time or can more easily interrupt hat they are doing, or who needs some 1:1 time with the baby. Cooking dinner is another matter, it's better to have an understanding of he will do it and when.
Good luck. It is all about communication, and about sharing expectations, even the ones that seem "totally obvious" to you, as they may be very obvious to him, as well, just in a very different way. And then about negotiating and compromising, and then every so often checking in with each other and evaluating how it is working for each of you, and what may need to be tweaked.
Never assume that the other person should know what you are thinking or feeling, he won't. Just as you cannot mind read either, and what your perception of his attitude or thoughts is can be far from the truth. We always see it through our own eyes, colored by our own experiences and history. If nothing else, that is something I have learned in my 20+ years of marriage. Not an easy lesson to learn, but a very valuable one! :-)
Best wishes for you all, and be sure you BOTH take time to just enjoy the baby - this time passes so quickly, but those memories and shared experiences are worth much more than a spotless floor in the long run.