My father just got back from abroad.

Literal

Father [topic-は] returned-to-country just-now [copula-だ].

~たばかりだ expresses that very little time has passed since the action. 帰国 is a compact Sino-Japanese compound (帰 return + 国 country) functioning as a suru-verb — a single word packing 'return to one's home country' into two characters.