I can't get my husband more involved in caring for our kids, and I want his help. What can I do?

It is also your husband's responsibility to take care and spend time with your kids, whether or not you both have jobs. Talk to him and make him aware that his involved will greatly impact the children's mental growth. So discuss the tasks you have to do and split them. Also ask him to spend quality time every week for relaxing with the kids and you.