Schoonhoven played a central role in the Nederlandse Informele Groep (Netherlandish Informel Group) and the Nul-groep (Nul Group), the Dutch equivalent of ZERO. Schoonhoven's work was included in various important group exhibitions including Zero-O-Nul at the Gemeentemuseum Den Haag, The Hague, in 1964, and Amsterdam, Paris, Düsseldorf at the Solomon R. Guggenheim Museum, New York, in 1972. Furthermore, he participated in documenta 4, Kassel, in 1968, and the IX Bienal de São Paulo, Brazil, in 1967, where he was awarded second prize.
Schoonhoven's work has been the subject of solo exhibitions at museums including the Gemeentemuseum Den Haag, The Hague, in 1967, and the Stedelijk Van Abbemuseum, Eindhoven, the Netherlands (1968, 1972, and 1973). Major exhibitions of the artist's work have been held in international institutions: in 1972, Jan J. Schoonhoven traveled from the Städtisches Museum, Mönchengladbach, Germany, to the Westfälischer Kunstverein, Münster, and the Museum van Bommel van Dam, Venlo, the Netherlands; in 1985–86, Jan Schoonhoven Retrospektiv: Tekeningen en reliëfs traveled from the Gemeentemuseum Den Haag, The Hague, to the Kunsthalle Nürnberg, Nuremberg, and finally to the Badischer Kunstverein, Karlsruhe, Germany; and in 1995–96, Jan J. Schoonhoven – retrospektiv traveled from Museum Folkwang, Essen, to the Bonnefantenmuseum, Maastricht, and the Aargauer Kunsthaus, Aarau, Switzerland.