In this sentence, the i sound in 'bayt-i-ha' is correct, unlike in 'bayt-i-hu' which's supposed to be pronounced as 'baytuhu'. That's because 'baytuhu' is at the beginning of the sentence (the nominative case), and 'bayt-i-ha' is preceded by مِنْ 'min' which's one of many Arabic prepositions that require the word that follows to have the i sound, which's كسرة kasra. (the genitive case).

Check the case lesson for more information.