Then please check the British ngrams comparison for high house and tall house. Maybe you will argue that both are awkward, but then, unfortunately, large or big wouldn't be good translations for the Czech sentence.
As a native English speaker, I disagree with you. A house is a physical structure. A home is where a family lives.
Try these sentences out: "House is where the heart is" "There's no place like house" "I love a good house-cooked meal" "What's your house-town?"
The different is subtle but significant, just like in Czech.