My kids' school has two K/1 classes and the parents of kids in the program really love it! At our school, they make sure the kids keep the same teacher for both grades. This is really great for the kids because when they start first grade the teacher already knows them really well and they don't have to spend weeks getting to know each other the way most kids do - they hit the ground running!
K/1 is great for kindergartners because they have the more mature and settled first graders to watch as examples for how to behave in school. It's great for the first graders because they get a chance to display some leadership skills as they "teach" the younger kids all about school.
Our two K/1 teachers also often divide the kids so that one teacher has all the kindergartners and the other has all the first graders. This is helpful for the more intense academic lessons. If your school does these two things (let kids stay with the same teacher for two years and team the teachers up so the kids get some time just with their own grade) I think this can be a really great thing for your kids.
Remember, in younger grades kids do most of their academic learning in small groups based on their abilities anyway, so it may not feel very different than a typical K or 1 class. And if you have a kindergartner who's very advanced or a first grader who's a bit behind, she'll have a great chance to hang out with kids at her level!
I do not agree with this. Kindergarten is/was supposed to introduce children to concepts. In other words, no real expectations would be placed on them. It was meant to be a positive program for children and promote school as a positive place. Some kindergartens accomplish while others can be failures. Combining these two grades is a huge mistake. Simply because the standards are higher in the first grade and learning objectives are clearly not the same.