One of my online doula acquaintances posted a string of links on FB about a technique called "Powerbirth" that midwives can be trained in by another midwife who is the founder (I am not including names here on purpose). Apparently it promotes some things that are not safe midwifey practices, including performing frequent vaginal exams and encouraging pushing at 5 cm while manually dilating the cervix, all of which pretty much must take place while the woman is on her back. The website of the creator of the method denies that promoting manual dilation, and claims that only "many," not "all" women experience an urge to push at 5 cm, but defends vaginal exams, claiming they "can give the midwife a wealth of information necessary to a good outcome for the mother and for the baby."
I certainly believe midwives who practice this way are a minority, but just be sure you ask the right questions, no matter who your provider is. A homebirth midwife is not guaranteed to have the same philosophy of birth you have.