I fell asleep before my dad got home.

Literal

I [topic-は] father [subject-が] return-come before [in-に] sleep ended-up.

Two clauses joined by 前に ('before'). The subordinate clause uses 帰ってくる ('to return [back home toward me]') — combining 帰る + くる to mark the directional 'come back here.' ~てしまった here marks 'ended up sleeping' with a hint of regret or unintended consequence (probably wanted to stay awake to see dad).