I'd like to suggest that one part of the problem may be in the way you're describing your husband's role at home. That word makes me wonder if perhaps the woman has defined the work of childrearing and housework as her role. It really helps to think about these questions so you can assess your situation more accurately. Talk to your partner about your concerns. As you talk, think about how you want to spend your time.
Most couples can handle the demands of a busy work life, a relationship, and a little housework.
They may occasionally get overburdened and stressed out, but they survive. Many couples find that they need to sit down and talk about the differences between their lives before and after parenthood, and to help one another understand that each has probably had to give up a lot of time that they used to take for granted. Ask him for help. Some fathers get involved in the care of their infants very early. They feel comfortable holding and soothing their babies and enjoy playing with them.