I've struggled with this one myself. What I do now is have my daughter, also in 1st grade, read me the assignment instructions. Then I have her tell me what it means in her own words to make sure she understands what to do. Once she's clear on what needs to be done then I move away from the table and go work on making dinner or dishes or whatever busy work I have to do in the kitchen.
If she has a question I will put it back to her as in "Well how do YOU think you could find the answer to the problem?" While I engage her in the thought process, I push her to utilize her own problem solving skills to come up with a solution.
After she has completed the assignment I will look over it with her and if I see something is wrong I ask her to review her answers to see if she can find her mistake. It may be something as simple as writing a letter or number backwards but I try to have her go find and fix it. Or sometimes it's because she forgot to use a math rule so she didn't get the correct answer. And still sometimes it's just something new and she hasn't quite gotten her mind wrapped around how it works yet.
If it's because she truly doesn't understand something than I work through it with her and attach a note to her teacher letting her know that M is struggling with this assignment and may need more help. Once the work is done to her satisfaction then we move on to the next subject's homework and follow the same procedure.
Just an FYI, our teacher told us at the beginning of the year if at any time your child is having difficulty completing an assignment include a note on that assignment or shoot her an email ASAP because if your child is struggling with it you can bet many others are too. She needs to know right away so she can reteach that lesson in a different way to make sure everybody understands before moving on to the next lesson.
Both of our teachers from last year and this year stressed the importance of the children doing their homework with very little assistance from us. They need to see how the kids do independently on their homework assignments to gauge their progress. Yes, they also use tests to see how the kids are doing but they are NOT testing every subject everyday. Our tests are given on Friday's so if they only went by testing then they wouldn't know until Friday that your child is struggling so by then they've wasted an entire week's teaching time on the subject. By using the homework as a guide the teacher can tell when the children are not understanding the work which gives her time to regroup and try teaching it in a different way.
Perhaps your husband could try just going over the instructions with her to make sure she comprehends what to do and then move away. Allow her to complete the assignment on her own and then check it with her.
Peace and Blessings,
T. B