Thomas has an email conversation with Eve Tushnet about using vouchers to send kids to Islamic madrassahs. The entire conversation, however, is inexorably pulled into orbit around the word "madrassah" itself, which is as heavily tainted as the word jihad, because of its misuse in popular media by non-muslims.
My community, the Bohras, have a madrassa in every city where we live. They meet on weekends, and the curriculum focuses on learning the arabic alphabet, memorizing religious songs and poetry about past leaders and events, and delving into the collection of hadith and Qur'an that are central to the underpinnings of our theologic school of thought.
In Houston, our community has so many children (over a hundred) that there is tralk of starting a "montessori". However, we still dont have the population density to support schools like the Burhani High School in Mumbai, which is open to students of all faiths but run by the Bohra clergy and which not only meets India's curriculum requirements, but whose students routinely test in the top percentiles. That too is a madrassa.
And there is of course the flagship, the Al-Jamea tus-Saifiyah, which is an Arabic Academy that not only trains students for religious leadership and volunteer roles in our community, but also imparts a full high-school equivalent curriculum including basic maths and sciences. You wont find classes on british literature, but why should there be any? For more info about The Jamea, see this entry from the Encyclopedia Of Islam, Oxford University Press.
All of these are types of madrassas. And thats only in the Bohra community, numbering 1 million adherents worldwide. The Nizari community, led by the Aga Khan, is ten times that number. My point is that reaction to the idea "vouchers might fund madrassahs!" is solely based on a narrow concept of madrassah which is NOT a majority in the Islamic world, especially in America, let alone worldwide. I think that we can apply the same standards to Islamic religious schools that we do to Christian or Jewish ones, to ensure that we arent funding white supremacists militias, messianic sayanim settlers, or suicide bombers.
 If you are interested in learning more about my community, the Dawoodi Bohras, I recommend this review of Mullahs on the Mainframe, by Jonah Blank.