“代表两党的”可以翻译为 “representing both parties” 或者 “on behalf of both parties” 。
例如：
He is a politician representing both parties in some cross-party initiatives.（他是一位在某些跨党派倡议中代表两党的政治家 。）
This agreement was reached on behalf of both parties.（这份协议是代表两党达成的 。）