"your house and his house"
Actually the audio is wrong here. It should be (baytuka wa baytuh).
The last vowel after (H) at the end of the sentence can be dropped because it is the end of the sentence. Assuming that there is something after that and speech need to be continued, then it would be (baytuhu); with -u added to the end. Both words here are nominative and not affected by a preposition and not being in accusative (a verb acting on them) so they should end in -u (bayt becomes baytu)- then followed by the suffices for your/masculine which (-ka) and for his/masculine (-hu). But as I said, at the end of the sentence, the last vowel on the last consonant in the sentence can be dropped as the sentence stops. It would be added if needed, to keep the speech affluent.