You asked

How can I get my husband to help around the house more?

You need to make it clear to your husband that looking after your child and managing the household is not solely your responsibility. Even if your husband is the only income provider it does not mean that you can only rely on him “helping out” when things get too much for you to handle. All fathers have responsibility that they must commit to when raising a child.
You need to examine the roles you both had before the baby was born; who did what around the house and who bore the responsibility for different facets of the household. Now that you have a small child, those responsibilities need to be re-examined. If you did the majority of the house work before your child was born, it won't be feasible for you to carry on doing the same workload under the new circumstances.
You need to discuss your feelings and concerns about the situation with your husband. Since looking after a baby is in itself a full-time job, more of the other responsibilities need to be taken over by your husband. Roles and responsibilities are changed after parenthood begins. Your husband needs to understand that his share of the work around the house is important and vital to the well-being of the family.
You should try to get your husband directly involved with looking after your child; holding and soothing, changing nappies, feeding with a formula bottle – these are all tasks your husband can and should do. Some dads are reluctant to get too involved in the early days, due to lack of experience and feeling incompetent. While some dads are forced into the deep end with looking after their baby, due to the mother having a caesarean, others will take time to adjust. You have to guide your husband and request aid when you need it; be specific with tasks that want done.
Give your husband time to learn parenting skills. Don't be impatient if things aren't done to your satisfaction at first. If you criticise every little mistake, your husband will lose interest in looking in the work assigned to him. With time and practice, a dad can do everything a mother can to look after a child – except breastfeed of course. The more time your husband spends looking after the baby, the better their bond will be. With new skills and a healthy relationship between father and child, you will be able to free up some time for yourself.
Make an effort to spend quality time with your husband. Discuss how things have changed and what you expect from the future. Find time between chores and tasks to have togetherness and quiet time. If you can afford it, or have a family member willing to help, arrange for a babysitter one night a week. This allows you time to talk and plan ahead for changes and to work as a team.

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