“房屋连地基”可以翻译为 "a house with its foundation" 或 "a house including its foundation"。
"a house with its foundation" 强调房屋与其地基作为一个整体存在。
"a house including its foundation" 则侧重于说明房屋的组成部分中包含地基。
根据具体语境，两者均可使用，但“a house with its foundation”更为简洁直接。