After finishing primary school and gymnasium in Karlovac, he graduated at the Faculty of Philosophy at the University of Zagreb the history of Yugoslav literatures, Croatian and Old Church Slavonic language and folk history with Russian and Latin. He spent two years (1930-1932) at the Charles University in Prague. Demonstrating the affiliation to literary and historical topics, he starts to translate from Czech. From 1933 he works as a professor at the gymnasium in Sušak, and in 1940 he relocates to Zagreb, where professor Stjepan Ivšić chooses him as an assistant in 1942. He was married to Nada Marković in 1940 with whom he had a daughter Dubravka and son Mladen (1944).
Simultaneously engaging himself in the topics of Croatian and Czech studies, he receives his Ph.D. with a thesis Dikcionar Karlovčanina Adama Patačića (Work of JAZU #274). From autumn 1945 he teaches Czech language and literature, and from autumn 1949 modern Croatian language at the newly-established department which he was a head from 1950, when he acquired the status of docent, up until the retirement in 1973. He became a regular professor in 1960. In 1950s Jonke engages in systematic study of a completely neglected subject of problems of Croatian language from the Illyrian times to the end of 19th century (Borbe oko književnog oblika imeničkog genitiva množine u 19. stoljeću, 1957.; Osnovni problemi hrvatskoga književnog jezika u 19. stoljeću, 1958; Sporovi pri odabiranju govora za zajednički književni jezik Hrvata u 19. stoljeću, 1959). He carefully examined the work of Bogoslav Šulek and Adolfo Veber Tkalčević.
He was a participant of Novi Sad agreement, styliser and the editor of "common" orthography, one of the editors of (also common) Dictionary of Serbo-Croatian literary language, member of JAZU. As soon as the applications of Novi Sad conclusions became detrimental at the expense of Croatian language, he publishes a series of polemics with Serb linguists and writers in which he defends the right of Croatian nation to its own language and the right of that language to achieve equal social status. He edited two columns of language advices (from 1961 in Telegram and since 1971 in Vjesnik), edited journal Jezik for 17 years, has been the vice-president of Matica hrvatska. In 1963 he was elected as a member of JAZU. Due to the alleged "Croat nationalism", having been denounced after signing the Declaration on the Status and Name of the Croatian Standard Language, and after the coup in Karađorđevo (1971) he was forcefully retired in 1973. Since then he has worked on the completion of JAZU dictionary. Jonke's main contribution (beside polemical and policital discussions in which he had done lion's share of fight against forceful Serbification of Croatian language) is in revitalising the interest to the contributions of Zagreb philological school and its essential role in the standardisation of Croatian language - a fact whose importance was often diminished and neglected for political reasons.