Father and mother are out shopping. Father and mother are out為系表結構，shopping為現在分詞，理解為作目的或伴隨狀語均可。

Father and mother are shopping out. Father and mother are shopping.為進行時態，out是副詞，表示地點狀語。

第一句比較多見；第二句比較鮮見，若改為Father and mother are shopping out in the street. 為佳，說明不是在商店購物，而是在外面的大街上，形成對比。