Both David Chipperfield Architects and Stanton Williams will go through to the next stage of the competition.
The pair will now face heavy competition from a number of high-profile Italian entrants, including Mario Botta and Guido Canali.
The project, commissioned by the Council of the Bassano Commune, will transform three historic buildings into public venues for the town centre.
A decision is expected by the end of 2005.
Both British practices have forthcoming projects in Padua, also in Italy. Early next year, Stanton Williams will commence work on the university's botanic gardens, after winning an international design competition.
A major exhibition showing 35 of David Chipperfield's projects opens at the town's Palazzo della Ragione on 19 November.
by Will Hunter