Yes, both must be covered by CSI and, as my current issue is teaching me, you should find out
exactly what CSI is from the German authority because there is no European precedent for this, thus every country will have different definitions of what is "comprehensive" (in my case, which is in Sweden, that means 100% coverage for everything, including previously known illnesses, accidents, riots, etc... which most private insurance companies don't cover).
However, if you are working in one country, but living in another, your partner may be covered under the national scheme of your home country. You can find more information
on the Europa website