Needing a visa and needing a passport are two different things. Generally speaking, you need a passport when going abroad. Many countries do treat transit differently when it comes to visa requirements but there is certainly no general exception to the passport requirement. 

That said, Turkey accepts ID cards (even for entry) for a handful of nationalities [including Switzerland](http://www.mfa.gov.tr/countries-whose-citizens-are-allowed-to-enter-turkey-with-their-national-id_s.en.mfa) but not, as far as I can tell, Bulgaria. There is [no need to get a visa for transit](http://www.mfa.gov.tr/frequently-asked-questions.en.mfa) either (provided you don't need to leave the “transit lounge” of the airport) and Bulgarian citizens can also [enter Turkey without a visa](http://www.mfa.gov.tr/visa-information-for-foreigners.en.mfa).

Consequently, it seems you could travel with only your Swiss ID, while your wife should take her passport with her but will not need any extra paperwork or payment (visa or e-visa). Note that the airline will check this before boarding the plane in Switzerland so you should probably ask them what they require for your trip (I heard about some people who had difficulties to convince the airline to let them take a flight to Turkey with an expired passport even though it's perfectly legal to enter Turkey with one in some cases).

(Your daughter also need some document but I assume she is also Bulgarian and/or Swiss so being on one of your passports or having a Swiss ID card should be enough – but I am not 100% sure.)